Using first-principles all-electron band structure method, we have systematically calculated the natural band offsets&Dgr;Evbetween all II–VI and separately between III–V semiconductor compounds. Fundamental regularities are uncovered: for common-cation systems&Dgr;Evdecreases when the cation atomic number increases, while for common-anion systems&Dgr;Evdecreases when the anion atomic number increases. We find that coupling between anionpand cationdstates plays a decisive role in determining the absolute position of the valence band maximum and thus the observed chemical trends. ©1998 American Institute of Physics.