Selfconsistent first principles calculations of the electronic structures of II-VI semiconductor compounds as well as of superlattices composed of alternating layers of II-VI compounds are presented. The importance of a proper treatment of the outermost d states and of relativistic effects is stressed. The superlattice calculations are used to derive valence-band offsets at interfaces and "absolute deformation potentials". The offsets derived from the self-consistent supercell calculations are compared to those obtained from the self-consistent supercell calculations are compared to those obtained by means of model theories ('dielectric mid-gap energy' model). Lattice matched as well as strained-layer systems are considered. © 1989.