The energy-band structures of {\mathrm{Cd}}_{3}$${\mathrm{As}}_{2}, {\mathrm{Zn}}_{3}$${\mathrm{As}}_{2}, and {\mathrm{Cd}}_{1.2}$${\mathrm{Zn}}_{1.8}$${\mathrm{As}}_{2} in a hypothetical fluorite structure have been determined, employing the pseudopotential method. From these results a qualitative picture of the band-edge structure in real crystals is deduced. It is shown that many optical and transport phenomena can be interpreted using these energy-band structures.