Nondeterminism in discrete-event systems occurs in many practical situations and often as a result of partial observability of events, For the adequate description of nondeterministic systems and nondeterministic phenomena, the trajectory-model formalism was introduced in [6] and [7]. This formalism has been used in [26] (also [14] and [15]) for obtaining various results on supervisory control of nondeterministic systems subject to language specifications. In the present paper we develop a theory of supervisory control for nondeterministic discrete-event systems subject to both language and trajectory-model specifications, We further show how well-known algorithms for supervisory control (of deterministic systems) under partial observation can be adapted for synthesis of supervisors for nondeterministic systems subject to both language and trajectory-model specifications.