The local empirical pseudopotential theory in the S-matrix implementation was used to study the structure of (Zn, Cd)(S,Se) polytypes considered as natural heterocrystalline superlattices. Hexagonal polytype superlattices of (Zn, Cd)(S,Se) are predicted to be characterized by direct band gaps and have minibands derived from evanescent bulk states, which collapse into the heterocrystalline interface bound states or resonances above the valence-band edge. There is a linear relationship between various band gaps and hexagonality h. The superlattice wave function is strongly localized in the cubic portions of superlattice unit cell.