This paper characterizes a class of hybrid systems that can be readily integrated with discrete event models and seamlessly simulated using available discrete event simulation software. We characterize this class of hybrid systems in terms of the Discrete Event System Specification, Hybrid Input/Output Automata, and as an event oriented simulation program. A small, but illustrative, example demonstrates the utility of these types of hybrid systems and the relative ease with which they can be incorporated into a discrete event simulation.