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We consider a distributed team decision problem in which different agents obtain from the environment different stochastic measurements, possibly at different random times, related to the same uncertain random vector. Each agent has the same objective function and prior probability distribution. We assume that each agent can compute an optimal tentative decision based upon his own observation and that these tentative decisions are communicated and received, possibly at random times, by a subset of other agents. Conditions for asymptotic convergence of each agent's decison sequence and asymptotic agreement of all agents' decisions are derived.