We provide a rigorous semantics for one of the central diagram types which are used in UML for the description of dynamical system behavior, namely activity diagrams. We resolve for these diagrams some of the ambiguities which arise from different interpretations of UML models. Since we phrase our definition in terms of Abstract State Machines, we define at the same time an interesting subclass of ASMs, offering the possibility to exploit the UML tool support for using these special ASMs in the practice of software design. We apply these Activity Diagram Machines for a succinct definition of the semantics of OCCAM.