The almost surely(a.s.)exponential stability is studied for semi-Markovian switched stochastic systems with randomly impulsive jumps.We start from the case that switches and impulses occur syn-chronously,in which the impulsive switching signal is a semi-Markovian process.For the case that switches and impulses occur asynchronously,the impulsive arrival time sequence and the types of jump maps are driven by a renewal process and a Markov chain,respectively.By applying the multiple Lyapunov function approach,sufficient conditions of exponential stability a.s.are obtained based upon the ergodic property of semi-Markovian process.The validity of the proposed theoretical results is demonstrated by a numerical example.