The stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics is investigated. For these Switching Markov Jump Linear Systems, mean square stability is analyzed through the time evolution of the second-order moment of the state. The main result is a sufficient condition that guarantees mean square stability under constraints on the dwell-time between switching instants. An alternative condition based on Kronecker calculus is worked out It is shown that both the stability criteria admit an LMI implementation (C) 2010 Elsevier Ltd. All rights reserved