There has been a great deal of interest in recent years in the use of service oriented approach and relevant standards to implement business processes. Following the concepts of workflow-based process management, the major focus has been on service composition. Not surprisingly, this default composition approach suffers from the limitations of centralized workflow management. It is well recognized that a decentralized execution setting where composed services can establish P2P interactions, is central to the management of a wide range of ubiquitous, mobile, large-scale and secure business processes. A natural way to enable the decentralized execution is to implement the relevant distributed cooperating processes of a centralized process on composed services. In this way, composed services can establish P2P interactions following the semantics of their processes. In this paper, we present a generic approach that enables decentralized executions with such cooperating processes. Precisely, we present our method that derives the latter. We focus on the sophisticated control/data flow and conversational aspects that run counter to naive intuition, most of which, we explain using deeper analysis of the algorithms and data structures that we employed.