This paper is concerned with the problem of robust stability for stochastic interval delayed additive neural networks (SIDANN) with Markovian switching. The time delay is assumed to be time-varying. In such neural networks, the features of stochastic systems, interval systems, time-varying delay systems and Markovian switching are taken into account. The mathematical model of this kind of neural networks is first proposed. Secondly, the global exponential stability in the mean square is studied for the SIDANN with Markovian switching. Based on the Lyapunov method, several stability conditions are presented, which can be expressed in terms of linear matrix inequalities. As a subsequent result, the stochastic interval additive neural networks with time-varying delay are also discussed. A sufficient condition is given to determine its stability. Finally, two simulation examples are provided to illustrate the effectiveness of the results developed.