In this paper we present a theory for decentralized supervisory control of a general class of multiprocess discrete event systems referred to as interacting discrete event systems (IDES). An IDES is a discrete event system that consists of a number of components working concurrently and possibly restricted by a well-defined interaction specification. We extend the notion of decentralized supervisory control to this class of systems by adding a supervisor for the interaction specification. Conditions that guarantee the optimality of the decentralized supervision of this class of systems are established and a complexity analysis of the proposed procedure is presented.