Abstract. We provide precise high-level models for eight fundamental service interaction patterns, together with schemes for their composition into complex service-based business process interconnections and interaction flows, supporting software-engineered business process management in multi-party collaborative environments. The mathematical nature of our models provides a basis for a rigorous execution-platform-independent analysis, in particular for benchmarking web services functionality. The models can also serve as accurate standard specifications, subject to further design leading by stepwise refinement to implementations. We begin by defining succinct rigorous models to mathematically capture the behavioral meaning of four basic bilateral business process interaction patterns (Sect. 1), together with their refinements to four basic multilateral interaction patterns (Sect. 2). We then illustrate with characteristic examples how by appropriate combinations and refinements of these eight fundamental patterns one can define arbitrarily complex interaction patterns of distributed service-based business processes that go beyond simple request-response sequences and may involve a dynamically evolving number of participants. This leads to a definition of the concept of process interaction flow or conversation,