Nuclear magnetic resonance (NMR) relaxation has been used to study molecular motion in binary systems of the molecular crystal hexamethylethane with several chemically distinct solutes in concentrations up to 10%. The anisotropic reorientation of HME molecules in the brittle phase is generally enhanced, but endospherical reorientation in the plastic phase is only disturbed by one of the solutes. Self-diffusion of HME molecules is reduced by one solute and enhanced by the others, but effects are small and the activation enthalpy is independent of solute concentration for the range studied. Possible explanations of the observed effects are discussed. The effects of the solvents on the phase transitions are also examined.