In Nolde Brothers, Inc. v. Local No. 358, Bakery & Confectionery Workers Union, AFL-CIO (1976), the Supreme Court ruled that an arbitration clause in a collective bargaining agreement could still be enforced even after the termination of the contract itself if the dispute arose from rights accrued or vested under it. The case involved Nolde Brothers Inc., a bakery company and its workers' union who had a disagreement over severance pay following termination of their collective bargaining agreement due to closure of business operations by Nolde Brothers Inc.. Despite contract termination, both parties were obligated to arbitrate this dispute because it was rooted in their expired agreement which contained an arbitration clause for any disputes arising out of interpretation or application of said agreement.

In the dissenting opinion for Nolde Brothers, Inc. v. Local No. 358, Bakery & Confectionery Workers Union, AFL-CIO (1976), Justice William Rehnquist argued that the majority's decision was incorrect because it failed to consider whether or not an arbitration clause in a collective bargaining agreement should continue after the contract has expired. He believed that this issue should be determined by examining each individual case rather than creating a blanket rule as done by the majority ruling. According to him, there is no reason why parties cannot negotiate and include specific terms regarding post-expiration disputes in their contracts if they wish to do so; however, without such explicit provisions present in an agreement, he did not believe it appropriate for courts to assume continued obligation of arbitration beyond contract expiration.