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This paper addresses the novel problem of recognizing digits spoken simultaneously by two different talkers. A factorial hidden Markov model architecture is proposed to accurately model the simultaneous utterance of two digits. Nadas' (1999) MIXMAX approximation is extended to a mixture of Gaussians observation PDF which enables the implementation of the proposed system. The multiple digit recognizer is found to successfully recognize pairs of simultaneous utterances of digits at 0db SNR with up to 89% accuracy.