The supervisory control of nondeterministic discrete event dynamical systems (DEDSs) with driven events in the setting of prioritized synchronization and trajectory models introduced by Heymann are studied. Prioritized synchronization captures the notions of controllable, uncontrollable, and driven events in a natural way, and the authors use it for constructing supervisory controllers, The trajectory model is used for characterizing the behavior of nondeterministic DEDSs since it is a sufficiently detailed model (in contrast to the less detailed language or failures models), and serves as a language congruence with respect to the operation of prioritized synchronization. Results concerning controllability and observability in this general setting are obtained.