Epitaxial CdSe layers were electrodeposited from aqueous solutions onto InP and GaAs single crystals. The analysis of current transients shows that the growth kinetics corresponds to the Scharifker model assuming a progressive nucleation followed by three-dimensional diffusion-limited growth. Diffusion control is effective after less than 0.1 s after the beginning of the potential pulse. The phenomena associated with the formation of a coherent film cannot be detected by this technique. Transmission electron microscopy observations of CdSe films with increasing thicknesses show when the diffusion control is effective, a large density of growth steps followed by the formation of epitaxial nuclei which finally coalesce.