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The decentralized partially observable Markov decision process (Dec-POMDP) is a powerful model for representing multi-agent problems with decentralized behavior. Unfortunately, current Dec-POMDP solution methods cannot solve problems with continuous observations, which are common in many real-world domains. To that end, we present a framework for representing and generating Dec-POMDP policies that explicitly include continuous observations. We apply our algorithm to a novel tagging problem and an extended version of a common benchmark, where it generates policies that meet or exceed the values of equivalent discretized domains without the need for finding an adequate discretization.