In this paper we investigate the use of action systems with differential actions in the specification of hybrid systems. As the main contribution we generalize the definition of a differential action, allowing the use of arbitrary relations over model variables and their time derivatives in modelling continuous-time dynamics. The generalized differential action has an intuitively appealing predicate transformer semantics, which we show to be both conjunctive and monotonic. In addition, we show that differential actions blend smoothly with conventional actions in action systems even under parallel composition. Moreover, as the strength of the action system formalism is the support for stepwise development by refinement, we investigate refinement involving a differential action. We show that, due to the predicate transformer semantics, standard action refinement techniques apply also to the differential action, thus, allowing stepwise development of hybrid systems.