The growth of ZnS and Zn1-xMgxS alloys on GaAs and GaP substrates oriented 2 degrees off the (1 0 0) in the [1 1 0] direction, using metalorganic chemical vapor deposition, is reported. The photoluminescence of high-quality ZnS samples is presented. Strain effects are considered to explain the valence band splitting, and the energy shift between ZnS/GaAs and ZnS/GaP photoluminescence spectra. For Zn1-xMgxS alloys, the composition as well as the optical and structural properties are investigated as a function of the growth parameters.