In this paper, for a class of switched stochastic (SS) systems, the moment stability (M-S) and sample path stability (SP-S) are investigated, respectively, and there are two main contributions. First, based on accurate estimations for the powers of solution of a special nonswitched stochastic (nSS) system, by employing the concepts of a Lyapunov function and describing the switching laws with the average dwell-time and the subsystems, three sufficiency theorems of p-th M-S are given for the SS systems. Then, for the SP-S of such systems, based on the results of p-th M-S, two sufficiency theorems are obtained for p > 2 and p = 2, respectively. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.