Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior (e.g., continuous-time dynamics, discrete-time dynamics, jump phenomena, logic commands, and the like) in different parts of a system are of great current interest (see, e.g., -). Typical examples of such systems of varying degrees of complexity include computer disk drives , transmissions and stepper motors , constrained robotic systems , intelligent vehicle/highway systems , sampled-data systems [lo]-[ll], switched systems -, and many other types of systems (refer, e.g., to the references included in [ 5 ] ) . Although some efforts have been made to provide a unified framework for describing such SYStems , most of the investigations in the literature focus on specific classes of hybrid systems. More to the point, at the present time, there does not appear to exist a satisfactory general model for hybrid dynamical systems which is suitable for the qualitative analysis of such systems. In the present paper we first formulate a definition of hybrid dynamical system which covers a very large number of classes of hybrid systems and which is suitable for the qualitative analysis of such systems. Next, we present several specific examples of hybrid dynamical systems. In a companion paper  we develop a qualitative theory which is based on the model for hybrid dynamical systems developed herein.