Epitaxial layers of ZnSe and ZnS were grown on (111) calcium fluoride (CaF 2) substrates in an open tube system by reaction of hydrogen with the compounds in powdered form. Typical growth rates of 1–2 μm h −1 for ZnSe and 3–5 μm h −1 for ZnS have been obtained. The parameters investigated were source temperature, substrate temperature and hydrogen flow rate. The experimental results were compared with theoretical growth rates calculated from the partial pressures of the components. In this case, the growth rate is proportional to the concentration difference between the source and the substrate and contains one adjustable parameter which depends on the substrate temperature and vapour phase composition.