Diffusion of a metal A in thin films consisting of a metal B was observed using the following two electron microscopy techniques: (1) observation of the growth of intermetallic phases with increasing concentration of A by the diffraction contrast of transmission micrographs and (2) recording of the distribution of A over the surface of the film by means of electron microprobe analysis. All experiments were carried out using a time dependency of the temperature of the form T(t)=T0(1+bt). The experimental results are interpreted by a simple theoretical diffusion model for the case of copper diffusion into palladium.