By fully exploiting service oriented architecture (SOA), Web service provides an efficient way to connect the existing on-line assets to support business enterprises. Most of the current Web service research inherently assumes that there exists only one service provider that can invoke those element services and compose them in a specific solution scenario. This paper aims to extend Web services research beyond the current limitations, allowing the existence of parallel and competitive service providers that compete for serving the customers. This paper intends to formally describe the concept of competitive Web service market, or CWSM in short. Web service composition problems pertinent to CWSM are also discussed. Two different models for CWSM are investigated, and the heuristics to be considered for the design of revenue oriented composition approaches are also proposed