Based on the sp(3)s* tight-binding method, the electronic band structures of both common-anion and common-cation II-VI superlattices (SLs) are investigated. As models, I took for the former one the case of CdTe/ZnTe(001) SLs, where the common anion is confirmed to yield a vanishing or a small valence-band offset (VBO). Here, the biaxial strain contributes in the valence-band splittings and yield type-I SLs in most of the studied cases. Whereas, I took as a second model two different SLs: the ZnS/ZnSe(001) and ZnSe/ZnTe(001) SLs. I have confirmed that the common-cation SLs cannot have a vanishing conduction-band offsets (CBOs), as speculated, but rather the CBO could be as large as the VBO. The biaxial strain, again, can participate here in the formation of the band offsets and yield either type-I SLs, as in the case of the ZnS/ZnSe, or type-II SLs, as in the case of ZnSe/ZnTe. Moreover, my theoretical results are compared to some available photoluminescence data and conclusions have been drawn about the strain morphology and the structural and optical qualities of the experimental samples. (C) 2004 American Vacuum Society.