This paper examines stochastic stability of switched dynamics in continuous time. The time evolution of the so called continuous state is at all times, determined by the dynamics indexed by the switching process or discrete state. The main contribution of this paper appears as stochastic stability results for switched dynamics with semi-Markovian switching. The notion of moment stability in the wide sense (MSWS) is applied as a generalization of c-moment stability. A sufficient criterion for MSWS is presented for the above class of systems, where each subsystem is assumed to be characterized by a Lyapunov function candidate together with an associated growth rate equation. For the set of Lyapunov functions, a compatibility criterion is assumed to be fulfilled, bounding the ratio between pairs of Lyapunov functions. (C) 2014 Elsevier Ltd. All rights reserved.