We present a summary of the results of an ab initio total energy study of t
he high-pressure phase diagrams of AlP, AlAs, and AlSb, calculated within t
he local-density-functional theory implemented within a pseudopotential sch
eme. Besides including structures considered in previous theoretical studie
s (zinc-blende, rock-salt, CsCl, NiAs, and beta-tin) we have also considere
d other structures such as Cmcm, cinnabar, and sc16, which have recently be
en found to be stable or metastable at high pressures in several III-V and
II-VI compounds. Our results support the stability of a Cmcm phase in a cer
tain range of pressure for each of the compounds studied.