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We study the decentralized control of discrete-event systems with multiple local specifications. Only a subset of events occur at a local site, and a local specification as well as control/observation capabilities of a local supervisor are defined with respect to such local events. The goal of control is to ensure that the executed behavior at each local site is as desired, i.e., there are multiple specifications, one for each site. We show that the control problem for multiple local specifications is different from that of a single global specification, and present a necessary and sufficient condition for the existence of decentralized supervisors for enforcing the given multiple local specifications. The synthesis of decentralized control for enforcing multiple local specifications is also presented. We also specialize our results to the case of concurrent plants (one which is composed of several local subplants), which offers certain computational savings. The results are illustrated through a simple manufacturing system example.