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This paper presents new results on the formal design of distributed coordinating agents in a discrete-event framework. In this framework, agents are modeled to be individually equipped with a coordination module, through which they interact and communicate. In terms of existing control-theoretic concepts, we first define the concept of a coordinable language and show that it is the necessary and sufficient existence condition of coordination modules for distributed agents to achieve conformance to a prespecified interagent constraint language. Following, we present a synthesis algorithm to compute near-optimal coordination modules. An example is provided to illustrate the design synthesis using the proposed algorithm. Finally, a discussion with related work distinguishes our coordination design problem from related problems in the literature.