Many cryptographic properties of m - valued logical functions are often described by their Chrestenson cyclic spectrums and auto-correlation functions, so Chrestenson cyclic spectrums and autocorrelation functions play important roles in properties and construct ions for m-valued logical functions. In this paper, in residue class ring Z_m, the concept of the strict avalanche criterion of order k of m-valued logical functions is presented. Then, by applying probabilistic thought and methods, the rule that a w-valued logical function fulfills the SAC of lower order if it fulfills the SAC of higher order is proved. Finally, by Chrestenson cyclic spectrums, a necessary and sufficient condition on a m-valued logical function is given, which fulfills the strict avalanche criterion of order k.