We present extensive theoretical calculations of the geometric and electronic properties of neutral and ionized III-V (Gap, GaAs, GaN, AlAs, and AIP) fullerene-like clusters of the type IIIxVx +/-4 with a number of atoms up to 52, on the basis of density functional theory. This study predicts the stability of heterofullerenes formed by all of these compounds, with the exception of GaN. We analyze the behavior of the energy gap and of the cohesive energy per atom as a function of the size and composition of the III-V fullerene and in comparison with previous theoretical calculations for BN fullerenes.