- Near singularities may occur in the electronic density of states of crystalline compounds under circumstances described in this paper. Such superdegeneracies are described as they result from simple Hckel treatments of various systems. Although these superdegeneracies are accidental in that they are broken when interactions ignored in the simple Hckel model are restored, large peaks in the density of states remain. The concepts presented are applied to both real and hypothetical cases. Superdegenerate bands are shown to invariably have a nonbonding character which can be fully understood only by consideration of the orbitals available for bonding in the extended structure. While the bands which cause superdegeneracies are flat, the Wannier functions associated with these bands cannot be well localized. The physical implications of this poor localization are discussed. In cases where superdegenerate bands are half occupied, ferromagnetic ground states appear to be favored. Analogies to molecular cases, where the importance of localizability of Hckel nonbonding molecular orbitals has already been closely examined, may point the way for the extension of this work beyond the simple one-electron treatment given here. 1985, American Chemical Society. All rights reserved.