  In a previous paper [\prb {\bf 50}, 1980 (1994)] we gave account of the
nondispersive band first found experimentally at --4.4 eV for CdTe(001) by
Niles and H\"ochst. We have characterized this band as a surface--induced bulk
state. In a second paper we showed that a similar state does exist in II--VI
and III--V zincblende semiconductor compounds. In this paper we show that there
are more such states within the valence band energy interval. We use
tight-binding hamiltonians and the surface Green's function matching method to
calculate the surface and surface--induced bulk states in the wide band gap
zincblende semiconductors CdTe, CdSe, ZnTe and ZnSe. We find a distinctive
surface state for the cation and two for the anion termination of the
(001)--surface and three (001)--surface--induced bulk states with energies that
correspond to the value of the heavy hole, light hole and spin--orbit bands at
$X$.
