We present a real-time execution semantics for UML activity graphs that is intended for workflow modelling. The semantics is defined in terms of execution algorithms that define how components of a workflow system execute an activity graph. The semantics stays close to the semantics of UML state machines, but differs from it in some minor points. Our semantics deals with real time. The semantics provides a basis for verification of UML activity graphs, for example using model checking, and also for executing UML activity graphs using simulation tools. We illustrate an execution by means of a small example.