Autonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi-player stochastic pursuit–evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties. In this paper, some fundamental issues of stochastic PE games are addressed. We first model a general stochastic multi-player PE differential game with perfect state information. To avoid the difficulty of multiplicity of the players, we extend the iterative method for deterministic multi-player PE games to the stochastic case. Starting from certain suboptimal solutions with an improving property, the optimization based on limited look-ahead can be used for improvement. The process converges when this improvement is applied iteratively. Furthermore, we introduce a hierarchical approach that can determine a valid starting point of the iterative process. As a basis for multi-player games, stochastic two-player PE games are also addressed. We also briefly discuss the games with imperfect state information and propose a suboptimal approach from a practical point of view. Finally, we demonstrate the usefulness and the feasibility of the method through simulations. Copyright # 2007 John Wiley & Sons, Ltd.