A switching diffusion is a typical example of a stochastic hybrid process, where the state (X(t),S(t)) of the system has a continuous component X(t) taking values in p a and a discrete component S(t) taking values in a finite set S := ~1, 2 , . . , M) . It arises in numerous applications of systems with multiple modes [16] such as in the hierarchical control of flexible manufacturing systems or large scale interconnected power networks [10]. See [1], [3], [6]-[16], [19] for relevant problems and applications. In this paper we discuss controlled switching diffusions as a particular class of hybrid control systems. This class of systems is also of interest in the study of deterministic hybrid systems, since deterministic hybrid systems can exhibit random behavior [9]. This work can be compared with the work of Branicky, et. al. for deterministic hybrid systems [7], [8]; our work allows less general jump rules and does not treat impulse control, but we are able to obtain very complete results for the cla~s of systems considered.