
529 N.W.2d 125 (1995)
3 Neb.App. 589
John BEAL and Joan Beal, Husband and Wife, Appellants,
v.
Marshall Bart ENDSLEY, Appellee.
No. A-94-637.
Court of Appeals of Nebraska.
March 28, 1995.
*126 Robert M. Brenner, of Robert M. Brenner Law Office, Gering, for appellants.
A. James Moravek, of Curtiss, Moravek & Curtiss, P.C., Alliance, for appellee.
SIEVERS, C.J., and HANNON and MUES, JJ.
MUES, Judge.
John Beal and Joan Beal, maternal grandparents of Nicholle and Tyler Endsley, appeal the decision of the district court for Box Butte County, claiming that the grandparent visitation rights granted to them on their petition filed pursuant to Neb. Rev.Stat. § 43-1801 et seq. (Reissue 1993) were not reasonable. Nicholle and Tyler are the children of the Beals' daughter, Jacquelyn Endsley, and Marshall Bart Endsley (Bart) and are in Bart's custody following the dissolution of the Endsleys' marriage. At the time of the hearing on the Beals' petition, Nicholle and Tyler were ages 13 and 9, respectively. We affirm the district court's *127 order as modified, and remand the cause with directions.

BACKGROUND
Bart and Jacquelyn are the divorced parents of Nicholle and Tyler. At the time of the hearing on the Beals' petition, Jacquelyn resided in the Denver, Colorado, area and Bart resided in Alliance, Nebraska. Nicholle and Tyler are in Bart's custody. This case was tried upon affidavits, as allowed by § 43-1802(2). The record is sparse on what Jacquelyn's visitation privileges are. It is clear that Jacquelyn has visitation with the minor children for the three "summer months." The record contains a letter dated December 23, 1992, proposing that Jacquelyn "have visitation with the minor children on the first and third weekends of each month from Friday evening to Sunday evening, with Jackie and Bart meeting half way to exchange the children at the beginning and at the end of each visitation" and that "the school holidays be alternated between Bart and Jackie," but there is nothing to indicate that this proposal was ever accepted or that this was, in fact, Jacquelyn's visitation schedule at the time of the hearing. There are a number of general references in the record regarding weekends that Jacquelyn was to have the children and to the "Memorial Day weekend which is already decided by the parties where the grandchildren are to go by the agreement of the parties," and Jacquelyn expresses that she has no problems as to whatever times may be set by the court insofar as her parents' visitation rights over her children, "as long as it is not over the Mother's Day weekend." Jacquelyn's "Voluntary Appearance" alleges that her visitation rights are set out by "the Court in her divorce proceedings." However, no order from the Endsleys' divorce proceedings is in the record before us.
The record does not indicate where Bart and Jacquelyn exchange the children on whatever visitations she might have. There is passing reference to Sterling, Colorado, as a location where Bart and Jacquelyn had exchanged the children at some unidentified point in time. The evidence discloses that the children had been exchanged on past grandparent visitations with Bart at "the 7-11 store in Wray," presumably a reference to Wray, Colorado.
In short, what we can glean from the record is that Bart and Jacquelyn were married and divorced; Bart has custody of their children and now lives in Alliance, Nebraska; Jacquelyn lives in Denver or Englewood, Colorado, and has visits of three summer months and certain weekends and holidays. The Beals live in Goodland, Kansas, where they moved from Alliance in June 1992, sometime after Bart and Jacquelyn were divorced. Bart is "on the road a lot," an apparent reference to Bart's employment. Jacquelyn had employment at some point, which has interfered with her visitation on occasion.
Pleadings and Parties.
The Beals filed their petition in Box Butte County, naming Bart as the sole defendant. The petition alleges that "since the divorce of the grandchildren's parents," the Beals had attempted to maintain a relationship with the grandchildren, but that these attempts had been unsuccessful, the differences between the parties becoming irreconcilable. The Beals allege that they had established a significant beneficial relationship with their grandchildren and allege that due to Bart's actions, the grandchildren had been limited in their ability to see their grandparents and spend time with them.
Jacquelyn was not named as a party in the Beals' petition and thus filed no answer, but a pleading captioned "Voluntary Appearance" was filed which contains a response to the petition. Therein, Jacquelyn
admits the allegations of the plaintiff [sic] petition as to a significant beneficial relationship and that the visitations with the minor children should be mutually shared by the parents. No adverse parent-child relationship will be affected by the granting of the visitations to the Plaintiffs. Her visitations are as set by the Court in her divorce proceedings, as amended by Court order thereafter. Transportation should be shared equally between the Defendant and Plaintiffs.
We digress, for a moment, to correct the caption in this matter to properly reflect that Jacquelyn Endsley is a party to these proceedings. Although not originally named, she did enter a voluntary appearance, *128 thus subjecting herself to the jurisdiction of the court. Although § 43-1803, the statute addressing the contents of a petition seeking grandparent visitation rights, does not specify who the proper parties defendant are, that section does require that the name of the custodial, as well as the noncustodial, parent of the child is to be set forth, and subsection (2) of that statute requires that a copy of the petition is to be served upon both. The relationship between parent and child is constitutionally protected, Quilloin v. Walcott, 434 U.S. 246, 98 S.Ct. 549, 54 L.Ed.2d 511 (1978), and proceedings which impact that relationship must afford both parents due process of law. In a petition filed pursuant to § 43-1801 et seq., in that circumstance where the grandchild's parents are divorced, both parents should be made parties to the proceedings.
Bart answered the Beals' petition, alleging an oral agreement between him and the Beals providing that they have visitation with the minor children "the last weekend of each month that had five weekends in the month" and alleging that Jacquelyn "has the children for visitation during the months of June, July and August which allows adequate time for visitation with Plaintiffs." Bart's answer goes on to allege various dates during 1993 that the Beals had visitations with the children and prays that the court award visitation consisting of "the last weekend of any month that has five weekends contained therein."
The Beals' reply to Bart's answer denies any agreement. The reply, made a part of the bill of exceptions through the Beals' affidavits, generally contests and explains the various allegations in Bart's answer regarding the Beals' time with the children during 1993.

FACTS
The sole evidence offered in this proceeding was the affidavits of John Beal, Joan Beal, Floyd Studer, Jacquelyn Endsley, and Bart Endsley. The evidence discloses a history of care and parenting that the Beals provided to their grandchildren. It also shows the problems with continuing the grandparent relationship since the Beals' move to Kansas in mid-1992 and the rejection by the Beals of Bart's proposal, through his attorney, with regard to specific grandparent visitation rights with Nicholle and Tyler.
Animosity and disagreements have existed between the Beals and Bart since July 12, 1992, an animosity which has continued from that point forward. Attempts on the part of the Beals to arrange visitation with Nicholle and Tyler have been less than satisfactorily received by Bart, although some have been accommodated.
The evidence further reflects that there are weekends when Jacquelyn, due to work scheduling or illness, could not exercise weekend visitations and where Bart has refused the request of Jacquelyn or the Beals for the Beals to have the children for that weekend. However, there is other evidence that the Beals were allowed visitation with their grandchildren on such occasions. Clearly, differences exist between the Beals and Bart regarding their visitation of the children and those differences have exacerbated since 1992, when they moved to Kansas.
The Beals sought the following visitation privileges: (1) Visitation one weekend every 6 weeks "in such manner as will alternate between the respective parents, a weekend that would affect each of them equally in terms of a visitation"; (2) one weekend alone each year with each separate child; (3) in September, the "grandparents' day weekend, which occurs generally on the 2nd weekend in September of each year," as well as Halloween; (4) notice of the children's school programs and special events and days off so that the grandparents can work out a time to be able to be present for these events; and (5) "whatever extended time during the summer for visitation with the grandchildren could be allowed."
The evidence strongly suggests it is the Beals' conviction that visitation "should be times taken equally from the Defendant [Bart] and from the daughter [Jacquelyn] so that the grandchildren have a meaningful relationship with the grandparents, as well as, the parents."
*129 As stated above, Jacquelyn generally has no opposition to whatever visitation the court may award her parents, so long as it does not interfere with Mother's Day weekend and she is not always the one forced to give up her time to accomplish it. Bart admitted the existence of a significant beneficial relationship between the Beals and the children and proposed that visitation be granted on the fifth weekend of each month having such a weekend.
District Court's Order.
The district court concluded that the Beals had established a significant beneficial relationship with Nicholle and Tyler. The court further found: "There is not a lot of time for visitation away from home when the mother exercises the visitation she is allowed. The Court is also in the opinion that taking visitation from the children's mother may not be best for the children."
Having said this, the court granted certain visitation to the Beals, requiring them to pay all costs for transportation for the visitations. The court's order provided:
Plaintiffs shall be allowed weekend visitation on the fifth weekend of any month that occurs. They shall also be allowed to exercise weekend visitation on any weekend or holiday that their daughter is allowed visitation with the children. They may also have visitation during the summer months with the minor children when the daughter has visitation with the minor children....
The court specifically found that "[t]o allow greater visitation would be a disservice to the children as their father has a duty to maintain some continuity in their lives." The Beals have appealed the order of the district court.

ASSIGNMENTS OF ERROR
The Beals allege two assignments of error. We view their second assignment as an argument in support of their single assignment of error, that being that the trial court erred in failing to award them reasonable grandparent visitation rights pursuant to § 43-1801 et seq. The Beals argue that the visitation rights granted were insufficient and that it was error for the trial court to order their visitation be exercised in conjunction with Jacquelyn's visitations.

STANDARD OF REVIEW
Determinations concerning grandparent visitation rights are initially entrusted to the discretion of the trial judge, whose determination, on appeal, shall be reviewed de novo on the record and affirmed in the absence of an abuse of the trial judge's discretion. Rosse v. Rosse, 244 Neb. 967, 510 N.W.2d 73 (1994); Dice v. Dice, 1 Neb.App. 241, 493 N.W.2d 207 (1992). See, also, Hickenbottom v. Hickenbottom, 239 Neb. 579, 477 N.W.2d 8 (1991).

DISCUSSION
The common-law view was that grandparents enjoyed no legal right to visitation with their grandchildren. In re Interest of Ditter, 212 Neb. 855, 326 N.W.2d 675 (1982). In 1986 Neb.Laws, L.B. 105, the Nebraska Legislature adopted a statutory procedure for grandparents to seek court-ordered visitation privileges with their grandchildren if, inter alia, the marriage of the grandchildren's parents has been dissolved. § 43-1802(1)(b). Section 43-1802(2) provides in pertinent part:
Reasonable rights of visitation may be granted when the court determines by clear and convincing evidence that there is, or has been, a significant beneficial relationship between the grandparent and the child, that it is in the best interests of the child that such relationship continue, and that such visitation will not adversely interfere with the parent-child relationship.
To succeed in obtaining a grant of visitation with grandchildren, grandparents have the burden to prove, by clear and convincing evidence, the following: (1) the existence of a significant beneficial relationship, past or present; (2) that it is in the best interests of the child that such relationship continue; and (3) that such visitation will not adversely interfere with the parent-child relationship. Once the grandparents have sustained that burden of proof, reasonable rights of visitation may be granted.
*130 The Beals argue that the issue on appeal is the reasonableness of the visitation rights granted by the district court. Bart admitted that a significant beneficial relationship exists between the Beals and their grandchildren and requested, at trial, the grant of certain visitation. The court's order expressly determined the existence of such a relationship and implicitly found that it would be in the best interests of Nicholle and Tyler that the relationship continue and that the visitation awarded would not adversely interfere with the parent-child relationship. Neither Bart nor Jacquelyn has cross-appealed.
Although § 43-1802 allows the district court to grant reasonable rights of visitation only after it is satisfied that the evidence is clear and convincing that the three conditions set forth above have been proven, the determination of what is reasonable visitation under the circumstances of each case necessarily requires the trial court to revisit consideration of the best interests of the children and the effect on the parent-child relationship in awarding specific visitation privileges. In other words, if a significant beneficial relationship exists, or has existed, between grandparents and grandchildren, it would naturally follow, by definition, that it would be beneficial for it to continue unless the "best interests" of the children, in the broader sense, suggest otherwise. Although certain visitation rights may not adversely affect the parent-child relationship, others most certainly would. Thus, the nature and extent of visitation granted is inextricably intertwined with the initial determination under § 43-1802 of whether such rights should be granted at all.
The Nebraska Legislature has clearly expressed the policy of this state regarding the importance of the parent-child relationship. Neb.Rev.Stat. § 42-364(1) (Cum.Supp.1994) provides that time spent with each parent following a divorce should be determined with the "objective of maintaining the ongoing involvement of both parents in the minor child's life." Section 43-1802(2) recognizes such policy by requiring that the grant of grandparent visitation be conditioned upon clear and convincing proof that such visitation "will not adversely interfere with the parent-child relationship." The grant of grandparent visitation necessarily involves a balancing of the superior parent-child relationship with the grandparent-child relationship.
We believe the overriding and paramount consideration in determining grandparent visitation rights under § 43-1801 et seq. is the best interests of the children. That standard is well settled as the benchmark in determining visitation rights between divorced parents. See § 42-364. See, also, Hickenbottom v. Hickenbottom, 239 Neb. 579, 477 N.W.2d 8 (1991); Gerber v. Gerber, 225 Neb. 611, 407 N.W.2d 497 (1987). There is no reason to suggest that the Legislature, in passing § 43-1801 et seq., intended to diminish the importance of that factor in determining the grant of grandparent visitation rights and the nature and extent of those rights.
In Gerber, the Supreme Court identified certain factors and circumstances properly considered in determining the nature and extent of parental visitation, recognizing that such visitation rights must be determined on a case-by-case basis. While recognizing that the factors set forth were not exhaustive or inflexible, the Gerber court pointed to such factors and circumstances as the age and health of the child; character of the noncustodial parent; the place where visitation will be exercised; frequency and duration of visits; the emotional relationship between the visiting parent and the child; the likely effect of visitation on the child; availability of the child for visitation; likelihood of disrupting an established lifestyle; and, in some circumstances, the wishes of the child. While recognizing the rights of parents to visitation as clearly superior, we believe the Gerber factors are appropriate considerations in determining whether to award grandparent visitation rights under § 43-1801 et seq., as well as the nature and extent of any such award, substituting, of course, "grandparent" for "noncustodial parent" or "visiting parent," as those terms appear in Gerber.
The Beals essentially challenge the visitation awarded on three grounds. First, they argue that the fifth-weekend visitation is simply insufficient because there are so few *131 fifth-weekend situations in a calendar year that it does not provide any meaningful opportunity for them to visit their grandchildren. Second, they contend that the court's order which says they "shall" be allowed to exercise visitation "on any weekend or holiday that their daughter is allowed visitation" contradicts the court's own finding that "taking visitation from the children's mother may not be best for the children" and is inconsistent with the legislative enactment in that it fixes the burden of sharing visitation upon the noncustodial parent, which is not lawful, fair, or just. Finally, they claim that the court's order which provides that the Beals "may also have visitation during the summer months ... when the daughter has visitation with the minor children" is purely discretionary and provides no assurance of any separate visits with the children.
Summer Visitation.
Discussing the last argument first, we agree that the court's order that the Beals "may" have visitation during the summer months leaves those visitation rights subject to agreement between the Beals and Jacquelyn. To that extent, it provides no definite visitation privileges. This portion of the "order" appears to represent more the reasoning of the district court in denying greater visitation to the Beals than an additional "award" of grandparent visitation. The relationship between the Beals and Jacquelyn appears to be good. The evidence reflects that in years past, the Beals have spent a significant amount of time with the children during the summer months, presumably during Jacquelyn's summer visitation. We take the Beals' argument on this point to simply be that they were not given sufficient separate visitation with their grandchildren by the court's order, a subject which we will address later in this opinion.
Weekend and Holiday Visitation.
With regard to the court's order that the Beals "shall" have visitation on weekends and holidays that Jacquelyn has visitation, we believe that this portion of the court's order was erroneous to the extent it purportedly creates visitation rights in the Beals which directly conflict with Jacquelyn's visitation privileges. "Shall" is a mandatory term. Although Jacquelyn's affidavit stated that she would "not have a problem as to times set up by the courts, as long as it is not over the Mother's Day weekend," thus suggesting that she would have no objection to giving up her weekends and holidays for the Beals, her affidavit also indicates that her visitations with the children are important to her and that she does not feel that she should "always be the one to give up my time with the children so that they may have visitation with their grandparents." It may be that the district court's use of the word "shall" in this portion of its order was inadvertent, in that it had clearly expressed the view that taking visitation from Jacquelyn may not be best for the children. Indeed, from the record, a more proper interpretation is that the court used the word "shall" in addressing visitation rights of the Beals during Jacquelyn's weekend and holiday visitations in order to clarify that in those instances where Jacquelyn was unable to exercise her visitation rights over the children, or was unable to pick the children up at precisely the designated time for visitation, the Beals, upon proper notice to Bart, were to be allowed visitation with their grandchildren. The record is replete with problems between the parties in those circumstances. In short, to the extent that the district court's order granted visitation rights to the Beals that superseded or conflicted with Jacquelyn's weekend and holiday visitation, it must be modified. We find that the district court's order should be clarified to express that the Beals' rights to visitation on Jacquelyn's holidays and weekends shall arise only on those occasions where Jacquelyn wishes her parents to exercise visitation or to assist her in her exercise of visitation with Nicholle and Tyler. In such circumstances, upon reasonable notice to Bart from Jacquelyn, consisting of at least verbal notice by phone no less than 24 hours before the visitation is to commence, Bart shall fully cooperate to allow the Beals such weekend and holiday visits as would have otherwise been due Jacquelyn, including such transportation arrangements as are applied to the Bart-Jacquelyn exchange of the children. We caution all parties that the parent-child visitation is paramount *132 and should be infrequently replaced in this manner.
Derivative Visitation.
The Beals generally argue that it was error for the district court to require that their visitation be exercised "principally in conjunction with" Jacquelyn's visitations. Brief for appellants at 19. This issue was assigned, but not discussed, by the appellant in Rosse v. Rosse, 244 Neb. 967, 510 N.W.2d 73 (1994), and thus the Supreme Court did not address it.
We do not believe that a hard-and-fast rule can be established in this regard. Some decisions from other jurisdictions suggest that grandparents' visitation with their grandchildren is sufficient if the relationship between the grandparents and their own child is not antagonistic and that the grandparents are given a reasonable opportunity to visit the grandchildren during their child's visitation time with the grandchildren. The cases cited by Bart for this proposition are ones where separate grandparent visitation was denied. See, e.g., Stricker v. Stricker, 474 So.2d 1146 (Ala.Civ.App.1985); Minns v. Minns, 615 S.W.2d 893 (Tex.Civ.App.1981). In Stricker, the appellate court affirmed the refusal to award separate visitation rights to a minor child's paternal grandmother. The grandmother lived in Colorado and the 6-year-old lived in Mobile, Alabama, with his mother. The grandmother's son, the noncustodial father, also lived in Mobile. The court noted that the grandmother frequently visited her son and could arrange to visit with her grandchild during the times that the father exercised his visitation rights. This was not a grant of grandparent visitation. It was an explanation for why grandparent visitation was being denied. Similarly, in Minns the appellate court affirmed the denial of visitation rights to the paternal grandmother, again noting that the father was allowed generous visitation privileges and there was nothing to suggest that the grandmother and her noncustodial son were antagonistic or, for any reason, were unable to share visitation. Yet there are other situations where, despite a good relationship between the grandparents and their child, and despite the grandparents' having visitation with the grandchild while visiting with the grandchild's parent, a grant of separate visitation has been found to be appropriate. In Pointer and Pointer, 112 Or.App. 511, 829 P.2d 1016 (1992), the appellate court rejected the custodial parent's argument that the grandparents' visitation should be confined only to those times when the child was visiting the grandparents' son, the noncustodial parent. Despite a good relationship and the opportunity to visit, the appellate court stated that it did not believe it was in the child's best interests to require the grandparents to visit only during the time that the child was with his noncustodial father, noting: "Father's time with the child is also important and is quite limited." Id. at 516, 829 P.2d at 1019.
It is one thing to award grandparents visitation rights during their child's visitation privileges with the grandchildren and quite another to deny visitation rights, recognizing that the grandparents already have adequate visitation privileges through the visitation schedule of their child with the grandchildren.
In the case before us, we believe the district court applied the rationale of both of the foregoing schools of thought. While recognizing that Jacquelyn and the Beals had a good relationship and that the Beals had the opportunity to maintain their relationship with Nicholle and Tyler during periods when Jacquelyn had them with her, as in Stricker and Minns, the district court also recognized, as in Pointer, that Jacquelyn's visitation time was important and thus granted the Beals separate visitation privileges, distinct from Jacquelyn's, although not as great as those sought.
Fifth Weekend.
We turn now to the Beals' contention that the court's grant of "the fifth weekend of every month that occurs" is patently insufficient. As stated above, in essence, this is the extent of the separate visitation granted by the court's order. The Beals argue that this is clearly insufficient as their only separate visitation because it is so infrequent and, even when allowed, the distance between Goodland, Kansas, and Alliance, Nebraska, *133 and the attendant travel time give them little opportunity to visit their grandchildren.
The Beals begin their argument by interpreting the word "weekend" as "both a Saturday and Sunday which has a numerical date in the same month." Brief for appellants at 16. They then go on to apply that definition to various calendar years as an illustration of just how little visitation this gives to them, i.e., 1994three weekends; 1995three weekends; 1996two weekends, etc. We believe the court's order is consistent with another interpretation, i.e., that the "fifth weekend" occurs in any month when there is a weekend which commences with a fifth Saturday and that it includes the following Sunday, whether it is in that same month or not. So defined, the Beals would have had visitations on five weekends for the year 1994; for 1995, four weekends; and for 1996, four weekends.
Rather than guess at what visitation the order was intended to grant to the Beals, we remand the matter to the district court with directions to clarify this portion of its order to more specifically define when a "fifth weekend" shall be deemed to occur and what it shall consist of, including the times and days of the week the Beals' visitation thereunder is to commence and to end.
Regarding the brevity occasioned by distance, we accept that the distance between Goodland, Kansas, and Alliance, Nebraska, will impact the Beals' visits with their grandchildren. The distance from Goodland to Englewood, Colorado, is also significant and it necessarily affects the Beals' ability to visit their grandchildren during Jacquelyn's visits with them. However, the children already travel extensively for visitations with Jacquelyn in Englewood, also a good distance from where the children reside in Alliance. The trial court's implicit conclusion that further disruption caused by more frequent separate visitations with the Beals would not be in the best interests of the children under the circumstances of this case is a wise one. The Supreme Court has often recognized the need for stability in the lives of young children. See, e.g., Kennedy v. Kennedy, 221 Neb. 724, 380 N.W.2d 300 (1986).
The district court, in rejecting the more extensive visitation sought by the Beals, noted the importance to the children of "continuity in their lives." Such reasoning evidences sound discretion, not an abuse of discretion. The disruption to the lives of the grandchildren, including the distance of travel to exercise visitation rights, is clearly an appropriate consideration in the award of grandparent visitation privileges under § 43-1802. See, also, Gerber v. Gerber, 225 Neb. 611, 407 N.W.2d 497 (1987). We cannot ignore that it was the Beals' move to Kansas which precipitated the visitation problems that are now being experienced. While they should not be penalized for such a move, neither should the Endsley children and their parents be forced to readjust their lives to accommodate the logistic problem created by such a decision. Finally, we note that the district court's order did not require that the Beals travel to Alliance to pick up Nicholle and Tyler. Rather, the court ordered that the Beals bear transportation costs for the visits. Presumably, options are available to mitigate travel time, provided the Beals wish to bear the expense.

CONCLUSION
To summarize, the Beals and their grandchildren, Nicholle and Tyler, obviously have a significant beneficial relationship. Jacquelyn and Bart both feel that it should continue, as did the district judge. We agree. The district court's order, while recognizing that the Beals have significant visitation opportunities with their grandchildren while they are with Jacquelyn during her times of visitation, also recognized that Jacquelyn's time alone with the children was critical. The "fifth weekend" visitation, clarified under either interpretation discussed, although not as extensive as that requested by the Beals, is a reasonable exercise of the trial court's discretion to fashion a plan of visitation taking into account all of the circumstances presented. The district court properly recognized the importance of the mother's separate visitation and the need for continuity and stability in the children's lives, while still allowing for separate visitation by the Beals.
*134 The district court's order is remanded to clarify the "fifth weekend" grant of visitation to the Beals and is otherwise affirmed as modified herein.
AFFIRMED AS MODIFIED, AND CAUSE REMANDED WITH DIRECTIONS.
