This paper presents the notion of time-coobservability as a core condition far the existence of a decentralized supervisor achieving a given language specification in a timed discrete event system (TDES). A TDES is modeled by the framework of Brandin & Wonham [5], and the decentralized supervisory control architecture presented is extended from the untimed architecture of Yoo & Lafortune [1]. To develop the time-coobservability of a language specification, specifically this paper presents the C&P time-coobservability and D&A time-coobservability in the consideration of the event tick and forcing mechanism of decentralized supervisors.