The dynamics of molecular associates in a methanol/water mixture was investigated using quasielastic neutron scattering. By measuring the signal from four methanol/water samples differing only by their isotopic composition, the relative motion of the water to methanol molecules, i.e. their mutual dynamics, was determined at the nanoscale. The thus obtained nanoscopic mutual diffusion coefficient signals a significantly slower process than the single particle diffusion of either methanol or water in the system as well as their macroscopic mutual diffusion. The data do not provide any indication of microsegregation in this preeminent alcohol/water mixture; however, they do indicate the existence of long lived but dynamic molecular associates of water and methanol molecules. Analysis of the structural relaxation shows that the lifetime of molecular association through hydrogen bonding determines the fact that viscosity of the mixtures at intermediate concentrations is higher than that of both pure components.