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For a system of distributed processes, correctness can be ensured by (statically) checking whether their composition satisfies properties of interest. However, Web services are distributed processes that dynamically discover properties of other Web services. Since the overall system may not be available statically and since each business process is supposed to be relatively simple, we propose to use runtime monitoring of conversations between partners as a means of checking behavioral correctness of the entire Web service system. Specifically, we identify a subset of UML 2.0 sequence diagrams as a property specification language and show that it is sufficiently expressive for capturing safety and liveness properties. By transforming these diagrams to automata, we enable conformance checking of finite execution traces against the specification. We show how our language can be used to specify the specification property system (SPS). We describe an implementation of our approach as part of an industrial system. Finally, we discuss our experience of specifying and monitoring a number of properties from three existing applications.