The energy and momentum relaxation of a nonequipartition gas mixture is considered. It is assumed that each component of the mixture has a Maxwellian distribution at a temperatureTi, with the peculiar velocity of the Maxwellian measured relative to the mean velocity of theith species. For the case in which a ``diffusion'' Mach number is not too large, the results have a particularly simple form. The calculations were carried out for the hard sphere, Coulomb, and Maxwell force laws of interaction. It is also noted how these results may be used to construct kinetic model equations for the case of hard sphere and Coulomb interaction, in a manner similar to that proposed by Sirovich.