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Multiple motion model (MMM) filters are a well-known approach for addressing rapidly maneuvering, noncooperative targets. Jump-Markov models provide the most well-known theoretical foundation for MMM filters. This paper addresses the problem of how to correctly generalize jump-Markov models to multitarget systems. Given this generalization, the jump-Markov version of the multisensor-multitarget Bayes filter is introduced. Then CPHD filter and PHD filter approximations of the jump-Markov multitarget Bayes filter are derived and compared with previous approaches.