  Based on a successful description of II-VI ternary alloys, which introduces
an empirical bowing parameter to the widely used virtual crystal approximation,
we set up a tight-binding Hamiltonian to describe the Zn_{1-y}Cd_ySe_{1-x}Te_x
and Zn_{.9}Cd_{.1}S_{.07}Se_{.93} quaternary alloys. We just use a formula that
can be thought as a straightforward generalization of the virtual crystal
approximation for this case. Our Hamiltonians reproduce very well the change in
the band gap value with the composition observed in recent experimental
reports.
