ZnTe and CdSe with lattice constants of 6.10 and 6.09 Å are nearly lattice matched to InAs with a lattice parameter of 6.06 Å. InAs is available as a high quality substrate material for molecular beam epitaxy (MBE). Reflection high energy electron diffraction (RHEED) and X-ray diffraction studies have been performed to investigate the nature of the MBE growth on InAs substrates with and without the epitaxial growth of an InAs buffer layer. For the quaternary Zn1 − xMgxSeyTe1 − y (ZnMgSeTe), we could tune the band gap through the whole visible range. Lattice matched to the InAs substrate, rocking curve widths as low as 38 arcsec for ZnMgSeTe could be obtained. We will present results on structural and optical investigations of these layers and related quantum well structures. A pronounced curvature in the dependence of the band gap on composition could be found not only for ZnSeTe and MgSeTe, but also for ZnMgSe and ZnMgTe. A type-II band alignment between ZnTe and ZnMgSeTe allows us to measure band offsets directly via photoluminescence measurements in particular single quantum well structures.