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The paper discusses a complete formalisation of UML state machine semantics. This formalisation is given in terms of an operational semantics and it can be used as the basis for code generation, simulation and verification tools for UML Statecharts diagrams. The formalisation is done in two steps. First, the structure of a UML state machine is translated into a term rewriting system. In the second step, the operational semantics of state machines is defined. In addition, some problematic situations that may arise are discussed. Our formalisation is able to deal with all the features of UML state machines and it has been implemented in the vUML tool, a tool for model-checking UML models.