Using the density-functional linear response method, we study dynamical ins
tabilities of the high-pressure CsCl phase in III-V semiconductors. For InS
b, we find no phonon instability that could prevent the CsCl phase from for
ming, consistent with the experimental observation. In contrast, for the mo
re ionic GaP, GaAs, InP, and InAs, we find that, while statically stable, t
he CsCl phase is dynamically unstable at high pressures with respect to tra
nsverse-acoustic [xi xi 0] phonons. Analysis of the soft normal modes via "
isotropy subgroup" suggests two candidate structures that will replace CsCl
structure at high pressure: the tP4 (B10) InBi type and the oP4 (B19) AuCd
type. Experimental examination of these predictions is called for.