The results of studying the effect of the characteristic size on the rate of diffusion processes in nanometer Cu-Ni film systems have been reported. The film system has been prepared by sequential vacuum deposition of the components, and the activation energy of diffusion has been determined from a change in the electrical resistance of the film system in a heating-cooling cycle. It has been shown that the activation energy of grain-boundary diffusion decreases with decreasing characteristic size of the system and amounts to 0.25 eV for the film system with a characteristic size of 5 nm, which corresponds to an increase in the grain-boundary diffusion coefficient by 10 orders of magnitude with respect to massive samples.