We define the dynamic semantics of UML State Machines which integrate statecharts with the UML object model. The use of ASMs allows us (a) to rigorously model the event driven run to completion scheme, including the sequential execution of entry/exit actions (along the structure of state nesting) and the concurrent execution of internal activities; (b) to formalize the object interaction, by combining control and data flow features in a seamless way; and (c) to provide a precise but nevertheless provably most general computational meaning to the UML terms of atomic and durative actions/activities. We borrow some features from the rigorous description of UML Activity Diagrams by ASMs in [7].