ZnS-based ZnMgSTe quaternary alloy layers have been grown by molecular beam epitaxy. The bandgap of ZnMgSTe has been estimated from the reflectance spectra, and it was found that it increases with increasing Mg content, while it decreases with increasing Te content. Nitrogen acceptor doping to Zn 1−x Mg x S 1−y Te y layers has also been investigated. The layers with Te content y > 0.1 were found to be p-type, and the layer with larger the Te content exhibits lower resistivity. From these