We consider the kinetics of tensile stress relaxation in thin metal film attached to inert substrate, controlled by chemical interdiffusion along the grain boundaries. We assume that the source of diffusing atoms is located at the surface of the film. We show that the kinetics of stress relaxation in the film can be either accelerated or slowed down if compared with the same kinetics in a single-component film, depending on the difference of intrinsic GB diffusion coefficients of the two components. In the case of faster matrix atoms, the tensile stress in the film significantly increases beyond its initial value at the beginning of interdiffusion process, while in the case of faster diffuser atoms, the compressive stresses develop in the film at the intermediate stages of stress evolution.