ZnSe epilayers have been grown on Se-induced reconstructed GaAs(0 0 1) surfaces. By varying the growth parameters such as substrate reconstruction, substrate temperature and atomic flux ratio, of Se to Zn, reflection high-energy electron diffraction (RHEED) observations have shown the most suitable growth conditions, in particular during the initial stages of ZnSe growth. Best results were obtained when, prior to ZnSe growth, zinc was deposited for 30s at a substrate temperature of 300 degrees C onto the Se-induced (2 x 3) reconstructed GaAs(0 0 1) surface. Remarkably the RHEED pattern did not show any evidence of a rough interface, instead there was a direct transition from a streaky GaAs pattern to a streaky ZnSe pattern. A detailed phase diagram concerning the common ZnSe(OO 1) surface reconstructions, i.e, the Se-rich (2 x 1) as well as Zn-rich c(2 X 2) reconstructions, was established as a function of the atomic flux ratio, of Se to Zn, and the substrate temperature.