本文分临界和非临界两种情形，建立了非线性时滞差分方程与其线性化方程振动性等价定理，推广和改进已有的工作．作为推论，修正了文[２］中主要定理的错误．

In this paper, it is shown that the nonlinear delay difference equation and its linearized equation have the same oscillatory behavior in the criticle case and noncritical case. The obtained results extend and improve the existing theorems in the literature. In the meantime, it also corrects the mistakes in the main theorem in [2].