
533 N.W.2d 103 (1995)
248 Neb. 202
Carroll E. EBERSPACHER and Margaret A. Eberspacher, Appellants,
v.
Tricia HULME and Rex A. Eberspacher, Appellees.
No. S-93-072.
Supreme Court of Nebraska.
June 9, 1995.
Gregory D. Barton, of Harding & Ogborn, Lincoln, for appellants.
Paul E. Galter, of Bauer, Galter, O'Brien, Allan & Butler, Lincoln, for appellee Hulme.
Charles M. Bressman, Jr., and Jeff C. Miller, of Young & White, Omaha, for appellee Rex A. Eberspacher.
*104 WHITE, C.J., CAPORALE, FAHRNBRUCH, LANPHIER, WRIGHT, and CONNOLLY, JJ.
LANPHIER, Justice.
Carroll E. and Margaret A. Eberspacher, the paternal grandparents of Shane and Matthew Eberspacher, petitioned the district court for Lancaster County for visitation rights with Shane and Matthew. The district court denied them visitation. The grandparents appealed to the Court of Appeals. The Court of Appeals reversed the district court and ordered visitation, finding that the district court had abused its discretion. Eberspacher v. Hulme, 1994 WL 718511, 94 NCA No. 51, case No. A-93-072 (not designated for permanent publication). We granted the petition for further review of Tricia V. Hulme, the children's mother. Because the record before the court demonstrates that the district court did not abuse its discretion, we reverse the judgment of the Court of Appeals and remand the cause to that court with direction that it reinstate the judgment of the district court.

BACKGROUND
Tricia Hulme and Rex A. Eberspacher were married in 1983 and had two sons, Shane and Matthew, before they divorced in 1989. After the divorce, Tricia Hulme was awarded custody of the children, and Rex Eberspacher was granted visitation. Rex Eberspacher's visitation included every other weekend, overnight each Wednesday evening, certain alternating holiday visitations, and a total of 3 weeks of summer visitation to be exercised 1 week at a time during the months of June, July, and August. Since the divorce, Tricia Hulme and Rex Eberspacher have been in nearly constant litigation regarding visitation.
At the time of the divorce, both Rex Eberspacher and Tricia Hulme lived in Omaha. Shortly thereafter, Rex Eberspacher moved to Parkville, Missouri, and Tricia Hulme moved to Grand Island, Nebraska. Carroll and Margaret Eberspacher live in Friend, Nebraska. In December 1989, Rex Eberspacher initiated a proceeding to modify the divorce decree. Rex Eberspacher's visitation rights were modified, based in part upon a stipulation and in part upon evidence adduced at trial. After the modification, Rex Eberspacher's visitation was one weekend per month, alternating holiday weekends to include the children's entire holiday vacation from school, and 35 consecutive days in the summer.
Shortly after this order became final, in April 1991, Tricia Hulme moved to Lincoln, Nebraska. Rex Eberspacher wanted expanded visitation. He then wrote Tricia Hulme, requesting that his visitation be informally modified. In this letter, Rex Eberspacher wrote the following:
In support of my desire to work out an agreement with you, I have asked my attorney to cease all pending litigations and hold-off on filing any petitions in response to the change of circumstances that has occurred recently with your move to Lincoln. I have asked mom and dad to hold-off in their pursuit of grandparents' rights as well.
In June 1991, Rex Eberspacher again filed an application for modification. Although the record does not reveal the outcome of this application, it is clear that visitation rights were not affected.
In May 1992, Carroll and Margaret Eberspacher filed a petition in the district court for Lancaster County seeking grandparent visitation rights pursuant to Neb.Rev.Stat. § 43-1801 et seq. (Reissue 1993). The petition seeking visitation and the subsequent action are the subjects of this appeal.
In their amended petition, the grandparents allege that a significant beneficial relationship exists; that it would be in the best interests of the children to allow the relationship to continue; that the granting of grandparent visitation would not adversely interfere with the parent-child relationship; and that they have tried to reconcile their differences, but Tricia Hulme refuses to enter into an agreement on the issue.
After a trial at which each of the parents and grandparents testified, the district court denied the petition. The district court determined that there was not clear and convincing evidence that there is or has been a *105 significant beneficial relationship between the grandparents and the children, that it is in the best interests of the children that such relationship continue, or that such visitation will not adversely interfere with the parent-child relationship.
After its thorough review of the record, the Court of Appeals came to the opposite conclusion, that "separate and reasonable visitation rights ... would serve the best interests of Shane and Matthew and would not adversely interfere with the parent-child relationship of either Tricia or Rex with the children." Eberspacher, 1994 WL 718511, 94 NCA No. 51 at 22. The Court of Appeals reversed the judgment of the district court, finding that the district court's denial of grandparent visitation was an abuse of discretion. It is from this order that Tricia Hulme appealed.

ASSIGNMENTS OF ERROR
In her petition for further review, Tricia Hulme asserts the Court of Appeals erred (1) in failing to recognize the trial court's discretionary authority under the pertinent statutes and (2) in failing to recognize that it was within the district court's discretion to decline to grant grandparent visitation because the petition was a collateral attack by Rex Eberspacher.

STANDARD OF REVIEW
Determinations concerning grandparent visitation are initially entrusted to the discretion of the trial judge, whose determinations, on appeal, will be reviewed de novo on the record and affirmed in the absence of abuse of the trial judge's discretion. Rosse v. Rosse, 244 Neb. 967, 510 N.W.2d 73 (1994).

ANALYSIS
In Nebraska, grandparent visitation is provided for by statute. Section 43-1801 et seq. Section 43-1802 provides, in pertinent part, the following with respect to grandparent visitation:
(1) A grandparent may seek visitation with his or her minor grandchild if:
(a) The child's parent or parents are deceased;
(b) The marriage of the child's parents has been dissolved or petition for the dissolution of such marriage has been filed, is still pending, but no decree has been entered; or
(c) The parents of the minor child have never been married but paternity has been legally established.
(2) In determining whether a grandparent shall be granted visitation, the court shall require evidence concerning the beneficial nature of the relationship of the grandparent to the child. The evidence may be presented by affidavit and shall demonstrate that a significant beneficial relationship exists, or has existed in the past, between the grandparent and the child and that it would be in the best interests of the child to allow such relationship to continue. 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.
It is within this statutory framework that we review the record and the respective conclusions of the lower courts. The statute plainly sets out three criteria for awarding grandparent visitation: (1) There is, or has been, a significant beneficial relationship between the grandparent and the child; (2) it is in the best interests of the child that such relationship continue; and (3) such visitation will not adversely interfere with the parent-child relationship. Each of the criteria must be proven by clear and convincing evidence before a court may grant grandparent visitation rights. However, even where each of the three criteria is proven by clear and convincing evidence, grandparent visitation is not mandated. The statute provides that reasonable rights of visitation may be granted when the criteria have been met. When the word "may" appears in a statute, permissive or discretionary action is presumed. Neb.Rev.Stat. § 49-802(1) (Reissue *106 1993). Thus, the statute gives the trial court discretion to make the determination.
At issue here is whether the district court abused that discretion in denying the Eberspachers grandparent visitation rights.
A judicial abuse of discretion exists when a judge, within the effective limits of authorized judicial power, elects to act or refrain from action, but the selected option results in a decision which is untenable and unfairly deprives a litigant of a substantial right or a just result in matters submitted for disposition through the judicial system. Cimino v. FirsTier Bank, 247 Neb. 797, 530 N.W.2d 606 (1995).
In light of the record, we cannot agree with the Court of Appeals that the district court abused its discretion in denying the petition for grandparent visitation. The record primarily consists of the testimony of Carroll, Margaret, and Rex Eberspacher and Tricia Hulme.
At trial, Carroll Eberspacher testified that when Rex Eberspacher and Tricia Hulme were married and living in Shelton, Nebraska, the grandparents went to visit the children at least once or twice a month. Later, when Rex Eberspacher and Tricia Hulme were living in Omaha, the grandparents visited about once a month. When the grandparents visit the grandchildren, they will take them to baseball games, to see fireworks, on walks, or just play with them. Carroll Eberspacher testified that currently he sees the children only on Rex Eberspacher's scheduled visitation. Carroll Eberspacher testified that he has called Tricia Hulme seeking visitation, but has always been denied. He testified that he says nothing disrespectful about Tricia Hulme in front of the children.
Carroll Eberspacher repeatedly testified that he would not have sought grandparent visitation if Rex Eberspacher would have received more time for visitation. Carroll Eberspacher stated that he does not think grandparent visitation will interfere with the children's relationship with their mother and father. He characterized his relationship with his grandchildren as a strong, beneficial relationship.
Margaret Eberspacher testified that she believes it would be in the children's best interests to have grandparent visitation awarded. She believes visitation will allow the children to love and trust their grandparents and get to know their extended family. She stated that she has a significant beneficial relationship with her grandsons. Margaret stated that she has not said anything derogatory about Tricia Hulme in the children's presence. She also stated that she is seeking visitation through the courts because Tricia Hulme never worked with them in any way toward agreeing to visitation.
Rex Eberspacher testified that he supports his parents' request for grandparent visitation. He stated that he believes the relationship between the children and his parents benefits the children because they learn to love others and are taught basic values of life by his parents. Rex Eberspacher testified that it was his opinion that grandparent visitation would not adversely affect the mother-child relationship.
With respect to whether he was the cause of his parents' suing for grandparent visitation, Rex Eberspacher testified that he "could have said" that he could have stopped his parents from pursuing visitation rights. Rex Eberspacher also stated that he discussed this action with his father before it was brought.
Tricia Hulme testified that she did not want the additional restrictions that court-ordered visitation would bring to her life and the lives of her children. She explained that she is willing to allow some type of visitation but does not want additional court-ordered restrictions. She testified that in her opinion the increased restrictions of grandparent visitation would not be in the best interests of her children. Tricia Hulme also testified about animosity that exists between her and the Eberspachers and also about some incidents illustrating the difficulties the animosity creates. Tricia Hulme testified that Carroll Eberspacher called her after he filed the petition for grandparent visitation and said, "`I see you got my little birthday card, huh?'"
The undisputed evidence of record is that the grandparent-grandchild relationship here *107 is an unremarkable, typical, healthy relationship. The district court, however, which observed the witnesses, did not find clear and convincing evidence that the relationship was such that it would be in the best interests of the children that it continue or that court-ordered grandparent visitation would not adversely interfere with the parent-child relationship. Even assuming the Court of Appeals was correctthat there was clear and convincing evidence of the three criteria required by § 43-1802we cannot say that the district court abused its discretion in denying the grandparents' petition, in light of the litigious relationship in this case.
There is evidence that the increased structure in the lives of Tricia Hulme and her children may be detrimental. Additionally, the adverse relationship between Tricia Hulme and Carroll and Margaret Eberspacher and the resulting incidents are evidence that ordered visitation may not be in the best interests of the children.
It is clear that the children's relationship with their grandparents will continue even though the petition is denied. There is nothing to suggest that Rex Eberspacher will not continue to share his allotted visitation with his parents. Rex Eberspacher's strong opinion of the value of his children's relationship with their grandparents seems to confirm that the relationship will continue despite denial of separate grandparent visitation.

CONCLUSION
The Court of Appeals erred in determining that the district court abused its discretion. We, therefore, reverse the judgment of the Court of Appeals and remand the cause to that court with the direction that it reinstate the judgment of the district court.
REVERSED AND REMANDED.
