Virtual Enterprises (VEs) are businesses providing services and products that rely on the resources of multiple enterprises. VEs can achieve their business objectives only through effective collaboration between the autonomous enterprises that comprise them. In this paper we advocate the position that effective multi-enterprise collaboration can be achieved by integrating the business processes of the participant enterprises, and by managing the resulting multi-enterprise (business) processes. A key requirement for this is developing multi-enterprise processes that explicitly capture and manage the functional and contractual relationships between the enterprises in a VE. In particular, this includes the inter-enterprise services each enterprise in a VE provides to others as needed to realize multi-enterprise processes. Current process management technology does not deal with the heterogeneity and autonomy of the processes that need to be integrated in a multi-enterprise process. In addition, existing solutions that combine services and multi-enterprise processes either lead to specification explosion or disallow conversations between process activities and services. The Collaboration Management Infrastructure (CMI) addresses these problems by extending an advanced workflow model with a comprehensive set of service management primitives. These include service interfaces, service activities, primitives for coordinating service activities, service wrapper processes, as well as service quality and contracts. A CMI system that supports these has been developed by integrating existing software components, such as a commercial workflow system, with several prototype engines and tools that support the new primitives for multi-enterprise process and service management. To illustrate how CMI supports these, we use multi-enterprise process and service examples from the telecommunications industry.