
591 N.W.2d 81 (1999)
256 Neb. 628
Gary Francis TRUMAN, Appellee,
v.
Barbara Ann TRUMAN, Appellant.
No. S-98-347.
Supreme Court of Nebraska.
April 2, 1999.
*82 Charles L. Caskey, Stanton, for appellant.
Michael J. Tasset, of Johnson and Mock, Oakland, for appellee.
Before: HENDRY, C.J., WRIGHT, CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ.
STEPHAN, J.
Barbara Ann Truman, now Barbara Ann Browne, appeals from an order of the district court for Madison County which determined that she was equitably estopped from collecting accrued child support from Gary Francis Truman, her former spouse. We find no error and affirm.

BACKGROUND
The marriage of the parties was dissolved by a decree entered by the district court for Madison County on May 6, 1976. Custody of the couple's two minor children, Dawn Marie Truman and Gary Francis Truman II, was awarded to Browne, and Truman was ordered to pay child support "in the sum of $26.00 per week per child being an initial total amount of $52.00 per week commencing April 10, 1976...." On October 9, 1997, Truman filed an "Application for Modification of Decree and for Correction of Child Support Records." An evidentiary hearing on this application was held on January 16, 1998. Truman testified at the hearing and offered documentary evidence which was received by *83 the court. Browne appeared through counsel, and although she was present in the courthouse during the hearing, she chose not to testify or offer any evidence. Thus, the facts summarized here are uncontroverted.
Following the dissolution of the marriage, Truman moved to Dodge County, Nebraska, and Browne moved to Montana with the children. In 1977, Browne initiated an action in Dodge County under the Revised Uniform Reciprocal Enforcement of Support Act (RURESA), Neb.Rev.Stat. § 42-762 et seq. (Reissue 1978), which has since been repealed. 1993 Neb.Laws, L.B. 500. On November 10, 1977, the district court for Dodge County entered a "Consent Support Order" requiring Truman to pay $40 per week in child support and $0 on arrearage to the clerk of the district court for Dodge County, who was required to transmit the payments to Browne through a court in Montana. This order contained no reference to the child support awarded in the Madison County decree.
In 1979, Browne filed another RURESA action in the district court for Colfax County, Nebraska, where Truman then resided. That court entered an order on March 8 requiring Truman to pay $160 per month in child support and $560 in arrearage, but continued the case until a later date to afford Truman an opportunity to submit evidence of child support payments he had made. Subsequent to the entry of this order, Truman received a letter from Browne stating that unless Truman agreed to assume custody of their son, she intended to place the son in an institution. Truman traveled to California where Browne was then residing and took custody of their then 4-year-old son, who has cerebral palsy. At that time, Truman and Browne reached a verbal agreement that because each parent would have custody of one child, neither would pay child support to the other in the future. On May 29, the district court for Colfax County entered an order in the pending RURESA proceeding which stated in part:
Upon the facts presented, it is hereby determined by this Court that Barbara Ann Browne has relinquished custody of her minor son to her former husband, Gary Frances Truman, and that she shall no longer require child support payments to be made by the said Gary Frances Truman. It is therefore ordered that this matter will be dismissed and that the said Gary Frances Truman pay all back support up to the date of June 1, 1979....
This order made no reference to the child support award contained in the original decree. Truman did not specifically request that his attorney obtain a modification of the decree to conform with his agreement with Browne and the resulting order of the district court for Colfax County, but he assumed that this had been done.
Browne made no effort to collect child support from Truman after relinquishing custody of their son to him. The son remained in Truman's custody until he reached the age of 21. The daughter continued to reside with Browne until her emancipation at the age of 17.
In 1990, Truman learned that child support under the terms of the original decree was accruing on the records of the clerk of the district court for Madison County. He consulted an attorney, who filed a petition for modification on Truman's behalf but then advised him to "wait and see." The record does not reflect that any action was taken with respect to the 1990 petition for modification. After Madison County officials initiated a wage garnishment proceeding based upon the delinquent child support reflected on its records, Truman commenced this proceeding in which he requested a modification of the original decree, to terminate his child support obligation as of June 1, 1979, as well as a determination of any arrearage due and the application of the wage garnishment as a credit against that amount.
Following the hearing, the district court determined that because modification of child support orders must be prospective, it did not have authority to reduce past-due installments of child support. However, the court concluded that under principles of equity, Browne was estopped from collecting any of the support that accrued after June 1, 1979. The court then calculated that Truman owed an arrearage in the amount of $1,846.80 and entered a judgment against Truman in that *84 amount. We removed Browne's appeal from this order to our docket on our own motion.

ASSIGNMENT OF ERROR
Browne asserts, restated, that the district court abused its discretion in determining that she was equitably estopped from collecting child support accruing after June 1, 1979.

STANDARD OF REVIEW
Modification of the amount of child support payments is entrusted to the discretion of the trial court, and although, on appeal, the issue is reviewed de novo on the record, the decision of the trial court will be affirmed absent an abuse of discretion. Faaborg v. Faaborg, 254 Neb. 501, 576 N.W.2d 826 (1998); Marr v. Marr, 245 Neb. 655, 515 N.W.2d 118 (1994).

ANALYSIS
Browne bases her appeal on certain established legal principles. The first is that the orders of the district courts for Dodge and Colfax Counties in the RURESA enforcement action initiated by Browne had no legal effect upon the award of child support contained in the 1976 decree of dissolution entered by the district court for Madison County. Former § 42-792 provided that a RURESA support order did not operate to nullify a previous support order "unless otherwise specifically provided by the court." The 1977 support order in Dodge County and the 1979 order entered in Colfax County made no reference to the 1976 decree entered in Madison County, and thus they did not alter its terms.
Browne also relies upon the well-established rule of law that when a divorce decree provides for the payment of stipulated sums monthly for child support, contingent only upon a subsequent order of the court, such payments become vested in the payee as they accrue, and generally, courts are without authority to reduce the amounts of such accrued payments. Wulff v. Wulff, 243 Neb. 616, 500 N.W.2d 845 (1993); Maddux v. Maddux, 239 Neb. 239, 475 N.W.2d 524 (1991). Parties in a dissolution proceeding cannot control the disposition of minor children by agreement. Stuhr v. Stuhr, 240 Neb. 239, 481 N.W.2d 212 (1992). Modification of an award of child support is not justified unless the applicant proves that a material change in circumstances has occurred since entry of the decree or a previous modification. Knaub v. Knaub, 245 Neb. 172, 512 N.W.2d 124 (1994); Wulff, supra. Where the requisite change in circumstances is established, the general rule in Nebraska has been to allow a modification of a child support order prospectively from the time of the modification order itself or, under some circumstances, retroactive to the filing date of the application for modification. Wulff, supra; Maddux, supra.
However, in Harrison v. Smith, 201 Neb. 21, 27, 265 N.W.2d 855, 859 (1978), this court recognized that the rule against modification of accrued child support applies "unless equitable estoppel is present." In that case, the child's mother was awarded custody in a 1952 decree. She subsequently remarried and, in 1957, obtained the written consent of the father to the adoption of the child by her husband, as well as the consent of the court which had issued the divorce decree. The adoption was never finalized, but this fact was not disclosed to the natural father until years later when the mother sought to collect the accrued child support. We held that under these circumstances, the mother was equitably estopped from recovering child support after the date when the adoption should have been completed. We wrote:
The application of a doctrine of equitable estoppel herein may seem to be a departure from the rule [that courts are without authority to reduce the amount of accrued child support]. That, however, is not the case. The divorce court, upon the petition of the mother and her then husband, gave its consent to the adoption. It made a specific finding that the father of the child had given his written consent to the adoption by the then husband of the mother. A further order should have been entered terminating future installments of child support. While the adoption proceedings pending in the county court were not thereafter completed, [the father] was not aware this had not been done. He had *85 every reason to expect they would be completed in a normal manner and that he would have no further responsibility for the support of his child.
Id. at 27-28, 265 N.W.2d at 860.
Subsequently, in Williams v. Williams, 206 Neb. 630, 294 N.W.2d 357 (1980), we reaffirmed the principle that the doctrine of equitable estoppel could operate to excuse the payment of accrued child support under appropriate factual circumstances. We stated that the elements of equitable estoppel are as follows:
"As to party estopped, (1) conduct which amounts to a false representation or concealment of material facts, or, at least, which is calculated to convey the impression that the facts are otherwise than, and inconsistent with, those which the party subsequently attempts to assert; (2) the intention, or at least the expectation, that such conduct shall be acted upon by, or influence, the other party or other persons; and (3) knowledge, actual or constructive, of the real facts; as to the other party, (4) lack of knowledge and of the means of knowledge of the truth as to the facts in question; (5) reliance, in good faith, upon the conduct or statements of the party to be estopped; and (6) action or inaction based thereon of such a character as to change the position or status of the party claiming the estoppel, to his injury, detriment, or prejudice."
Id. at 637, 294 N.W.2d at 362, quoting Chappelear v. Grange & Farmers Ins. Co., 190 Neb. 589, 210 N.W.2d 921 (1973). See, also, State on Behalf of Hopkins v. Batt, 253 Neb. 852, 573 N.W.2d 425 (1998).
Although this court has not previously examined the applicability of equitable estoppel under the circumstances presented in this case, other courts have applied the doctrine where parties agree to a relinquishment of custody or visitation rights in exchange for termination of child support, but do not obtain the necessary judicial approval. For example, in In Re Marriage of Webber, 191 Ill.App.3d 327, 547 N.E.2d 749, 138 Ill.Dec. 582 (1989), a mother was held to be estopped from collecting accrued child support for a period during which she had voluntarily relinquished custody to the father and agreed to waive his child support obligation. The court determined that "[i]n becoming the custodial parent of his son and providing for his son's needs while he lived with him," the father incurred a legal detriment in reasonable reliance upon the mother's agreement. Id. at 331, 547 N.E.2d at 752, 138 Ill.Dec. at 585, Similarly, in In re Marriage of Harms v. Harms, 174 Wis.2d 780, 498 N.W.2d 229 (1993), the court held that where a mother removed the children in her custody from the state where the father resided, advised him in writing that she no longer expected him to pay child support, and took no legal action to enforce the original child support obligation for a period of 7 years, she was estopped from collecting accrued child support. The court reasoned that the father stopped making child support payments in reliance upon the mother's statements and gave up his right to challenge the children's removal from the state, which inhibited his visitation rights. See, also, State v. Stephen Leo S., 198 W.Va. 234, 479 S.E.2d 895 (1996) (holding that extrajudicial agreement of parties regarding termination of child support obligations was enforceable under doctrine of equitable estoppel where welfare of children not adversely affected); McNattin v. McNattin, 450 N.W.2d 169 (Minn.App.1990) (holding that mother's extrajudicial agreement not to seek child support in exchange for father's agreement to relinquish custody of child to her not binding upon court but was enforceable under doctrine of equitable estoppel).
We conclude that the uncontroverted facts support the application of equitable estoppel in the present case. When Browne relinquished custody of the parties' son to Truman in 1979, she agreed that Truman would not be obligated to pay child support in the future. Her intent and expectation that the agreement would be acted upon is established by the 1979 order of the district court for Colfax County making specific reference to the agreement and dismissing the RURESA proceeding which Browne had initiated. This order accurately reflected the parties' agreement but inexplicably did not include language which would have terminated the accrual of child support on the records *86 of the district court for Madison County. It is apparent that Truman relied in good faith on this order and on his agreement with Browne in that he changed his position by assuming responsibility for the custody and care of the parties' son for the remainder of the son's minority and, in fact, thereafter. Although she had filed two enforcement actions under RURESA within 3 years of the dissolution, Browne made no effort to collect child support during the period of approximately 17 years which transpired between the entry of the order in Colfax County reflecting the parties' agreement regarding the termination of Truman's obligation to pay child support and the initiation of this proceeding by Truman. There is no evidence that the agreement of the parties was in any way detrimental to the welfare of the children, who have both reached the age of majority. We agree with the district court that under these circumstances, it would be patently inequitable to require Truman to pay child support accruing after June 1, 1979.
For these reasons, we find no abuse of discretion by the district court and therefore affirm its judgment.
AFFIRMED.
