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We show that composite fermi/bose superfluids can be created in coldatom traps by employing a Feshbach resonance or coherent photoassociation. The bosonic molecular condensate created in this way implies a new fermion pairing mechanism associated with the exchange of fermion pairs between the molecular condensate and an atomic fermion superfluid. We predict macroscopically coherent, Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the molecular energy, and suggest that these oscillations will provide an experimental signature of the pairing. PACS numbers(s):03.75. Fi, 05.30.Jp, 32.80Pj, 67.90.+z Typeset using REVT E X

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