This paper deals with the stochastic stability problems for the certain and uncertain neutral and Markovian jump systems with two additive time-delays. Time delays are considered as both stochastic and time-varying, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functional, the sufficient conditions are obtained to guarantee the stochastic stability for the certain and uncertain systems. To show an application of the systems, we develop the teleoperation systems which have the forward and backward transmission time delays and give a numerical example to illustrate the effectiveness of the developed method.