Epitaxial growth of cadmium selenide on ((111) over bar) InP single crystals is achieved by chemical bath deposition in cadmium sulfate and sodium selenosulfate solutions complexed by sodium nitrilotriacetate. Correlations are established between the growth mechanism, studied by means of a quartz crystal microbalance, and the CdSe epitaxial quality evaluated by means of x-ray diffraction and electron microscopy. It is shown that the formation of CdSe films can be described by a layer-by-layer mechanism. Correlatively the epitaxy of CdSe on InP substrates occurs when the thickness of each layer is close to one lattice unit. Epitaxial CdSe layers present a cubic blende structure with a density of twins which depends on the growth conditions.