We describe a logical system and methodology for the natural specification of nondeterministic actions. The logic combines elements of dynamic logic, process logic and the situation calculus and allows one to express alternative ( actual and possible) paths or sequences of events. Our system permits a simple solution to the frame problem for nondeterministic actions that ``completes'' user-supplied theories of action. While drawing inspiration from Reiter's solution for the deterministic case, some of the main intuitions underlying this solution must be abandoned in the nondeterministic setting due to possible correlations among effects. We show our completion is unambiguous and faithful to our stated intuitions, and that in a deterministic setting our solution is equivalent to that of Reiter.