Epitaxial CdSe films have been electrodeposited on the (100) face of InP and GaAs single crystals. The quality of the epitaxy and chemical composition of CdSe films have been investigated by reflection high-energy electron diffraction, X-ray diffraction and XPS measurements. A good stability of the InP and GaAs surfaces, in presence of the deposition electrolytes, was found. The choice of the deposition parameters is crucial for the growth of epitaxial and stoichiometric layers.