Summary: 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. This formalism has been used in [\textit{M. Shayman} and \textit{R. Kumar}, SIAM J. Control Optim. 33, No. 2, 469-497 (1995; Zbl 0819.93003)] 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.