In networked control systems, uncontrollable events may unexpectedly occur at a plant before a proper control command is applied to it due to communication delays. In this paper, we address the problem of decentralized supervisory control under such communication delays based on the C&P (conjunctive and permissive) and D&A (disjunctive and antipermissive) decision architecture. In particular, for the existence of a decentralized supervisor, we present the notion of delay-coobservability of a given language specification and a polynomial-time algorithm for verifying it. In addition, algebraic properties of the delay-coobservability are investigated. We further present a synthesis method of the decentralized supervisor for practical usefulness. (C) 2009 Elsevier Ltd. All rights reserved.