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In this paper, we consider diagnosability of discrete event systems with simultaneous event occurrences, which we call concurrent discrete event systems. The systems have a problem that the number of event sets, which may occur concurrently, is increasing exponentially. So, it is difficult to design a diagnoser. We introduce a notion of concurrent well-posedness (CWP). We then prove that CWP is a necessary and sufficient condition for no effect of concurrency on the diagnosability in concurrent discrete event systems.