A fundamental feature of service oriented computing is that simple services need to be composed for generating complex services. This work focuses on the analysis and verification of behavior models of web services composition. In particular, we have to check that neither deadlock nor livelock occurs in this composition. Usually, the verification of such integration, with or without mediators, is achieved by using techniques based on state space exploration of a given service formal model. In this paper, we present an approach based on structure theory of Petri nets allowing the recognition of necessary and/or sufficient conditions ensuring compatible composition and a better understanding of the incompatibility sources.