This paper presents supervisory control theory in a process-algebraic setting, and proposes a way of synthesising modular supervisors that guarantee nonblocking. The framework used includes the possibility of hiding actions which results in nondeterminism. As modularity crucially depends on the process equivalence used, the paper studies possible equivalences and points out that, in order to be consistent with respect to the nonblocking property and to supervisor synthesis, a conflict-preserving equivalence must be used. It applies the results to synthesise nonblocking modular supervisors for a manufacturing system.