This paper considers the robustness of stochastic stability of Markovian jump linear systems in continuous- and discrete-time with respect to their transition rates and probabilities, respectively. The continuous-time (discrete-time) system is described via a continuous-valued state vector and a discrete-valued mode which varies according to a Markov process (chain). By using stochastic Lyapunov function approach and Kronecker product transformation techniques, sufficient conditions are obtained for the robust stochastic stability of the underlying systems, which are in terms of upper bounds on the perturbed transition rates and probabilities. Analytical expressions are derived for scalar systems, which are straightforward to use. Numerical examples are presented to show the potential of the proposed techniques. (c) 2006 Elsevier Ltd. All rights reserved.