Models of distributed software systems extend naturally to cyber-physical systems “in the large”; i.e., systems of loosely coupled software components which interact with models of physical processes. But how do we model such combined systems? This paper discusses this problem from the perspective of active object systems. We attach different active objects to models of physical systems, but maintain the objects’ actor-like decoupling of communication and synchronization. The result is a model of hybrid active objects. In this setting, we discuss different ways of modeling and controlling time advance and value propagation between components, which may be inside the model, controlled by the model, or controlling the model as a simulation unit. The patterns of on-demand value propagation as well as fixed- and variable-step time advance arise naturally from the semantics of hybrid active object models in HABS, a hybrid extension of the formal specification language ABS.