中文摘要：

这篇论文与片涉及理论答案和非线性的微分方程的一个班的数字答案的稳定性明智的延期。起初，为这些问题的理论答案的稳定性的一个足够的条件被给定的、然后数字的稳定性和 asymptotical 稳定性为一个类被讨论当适用于这些问题时，多走方法。

英文摘要：

This paper is concerned with the stability of theoretical solution and numerical solution of a class of nonlinear differential equations with piecewise delays. At first, a sufficient condition for the stability of theoretical solution of these problems is given, then numerical stability and asymptotical stability are discussed for a class of multistep methods when applied to these problems.