AbstractObject-Based Graph Grammar (OBGG) is a formal visual language suited to the specification of asynchronous distributed systems based on message passing. Model-checking of OBGG models is currently supported and a series of case studies have been developed. However, in many situations one has to evaluate non-functional aspects like availability and performance of the system under consideration. In such cases, a stochastic analysis of the system is desired. This paper is a first contribution to the stochastic analysis of OBGG models. OBGG models with occurrence rates associated to rules are translated to Stochastic Automata Networks (SAN). SAN is a Markov Chain equivalent formalism having as advantage its modularity in terms of representation and a compact mathematical solution, allowing the analysis of models with larger state space.