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Maximum likelihood detector algorithms are developed for the matrix of transmitted symbols in a multiuser system in which the received signal is the sum of K cochannel continuous phase modulated (CPM) signals and additive white Gaussian noise. We illustrate that the maximum likelihood matrix detector, which provides optimum detector performance, consists of K sets of front-end matched filters followed by a Viterbi algorithm. We also derive two reduced complexity receivers, demonstrating through simulation that they perform within 1-2 dB of the optimal while substantially reducing complexity. The paper demonstrates how performance can be traded off against complexity, giving particular attention to cochannel Gaussian minimum shift keyed (GMSK) signals