A theoretical investigation has been carried out on several group III-V (13-15) four-membered-ring compounds which, if experimentally attainable, are potentially useful as precursors to nanocrystalline electronic and semiconductor materials. Four-membered-ring compounds considered in this study have core structures of the following form : MEM’E’ and MEMX (M, M’ = In, Ga, Al; E, E’ = P, As; X = Cl, Br). Equilibrium geometries, binding energies, and bond energies were determined based on local density approximation (LDA) and gradient-corrected density-functional methods. Optimized ring geometries obtained with LDA agree closely with single-crystal X-ray crystallographic structures of known compounds with the same four-membered-ring cores. The following trends in bond energies are observed : M-Cl much greater than M-P > M-As much greater than M-Br (M = In, Ga, Al), and Al-Y > Ga-Y > In-Y (Y = P, As, Cl, Br). Although only one M-Br-containing mixed-bridge four-membered-ring compound has been reported and no such Al-Cl-containing mixed-bridge species have yet been synthesized, our calculations suggest that compounds containing these two ring systems are stable.