In a previous paper [15], we showed that supervisory control of nondeterministic discrete event systems, in the presence of driven events, can be achieved using prioritized synchronous composition as a mechanism of control, and trajectory models as a modeling formalism. The specifications considered in [15] were given by prefix-closed languages. In this paper, we extend the theory of trajectory models and prioritized synchronous composition to include markings so that non-closed specifications and issues such as blocking can be addressed. It is shown that the usual notion of non-blocking, called language model non- blocking, is inadequate in the setting of nondeterministic systems, and a stronger notion, called trajectory model non- blocking, is introduced. Necessary and sufficient conditions for the existence of non-marking and language model non-blocking as well as trajectory model non-blocking supervisors is obtained for nondeterministic systems in the presence of driven events. We also show that our approach is also suitable for modular supervisory control.