The recent approaches for Web services composition tend to integrate heterogeneous business processes executed in Peer-to-Peer networks. In such networks, componentWeb services are invoked on independent peers and are orchestrated according to the transactional requirements defined by the designers or the users of the composite Web service. Since component Web services can be dynamically invoked and are generally implemented as black boxes, concurrency between them may appear. This paper presents the transactional execution model of compositeWeb services exploiting the transactional properties of their component Web services. The proposed concurrency control is ensured by a decentralized serialization graph based on an optimistic protocol and on the hierarchical structure of the composition. The globally correct execution of the composite Web service is achieved by communication among dependent subtransactions and the peers they have accessed.