Asynchronous cellular automata and asynchronous automata have been introduced by Zielonka [14] for the study of Mazurkiewicz traces. In [2] Droste & Gastin generalized the first to pomsets. We show that the expressiveness of monadic second order logic and asynchronous cellular automata are different in the class of all pomsets without auto-concurrency. Then we introduce a class where the expressivenesses coincide. This extends the results from [2]. Furthermore, we propose a generalization of trace asynchronous automata for general pomsets. We show that their expressive power coincides with that of monadic second order logic for a large class of pomsets. The universality and the equivalence of asynchronous automata for pomsets are proved to be decidable which is shown to be false for asynchronous cellular automata.