Stochastic Well-formed Nets (SWNs) are a Petri Net model which allows the computation of performance indices with an aggregation method. Decomposition methods initiated by Plateau are another way to reduce the complexity of such a computation.We have shown in a previous work, how to combine these two approaches for systems with synchronous composition. Despite similarities between the asynchronous and synchronous cases, it turns out that the former presents specificities that need theoretical foundations. We undertake this task in the present paper. We derive necessary conditions on the modelled systems that allow for the two methods to be combined. For parallel systems satisfying these necessary conditions, we develop a model with the corresponding algorithm. This model, based upon synchronization of " global " tokens moving across submodels, covers a large range of real life systems. An example shows the intuitive ideas behind these developments.