An action system framework is a predicate transformer based method for modelling and analysing distributed and reactive systems. The actions are statements in Dijkstra’s guarded command language, and their semantics is given by predicate transformers. We extend conventional action systems with a differential action consisting of a differential equation and an evolution guard. The semantics is given by a weakest liberal precondition transformer, because it is not always desirable that differential actions terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero.