Ab initio molecular quantum mechanics has been used to study the potential energy surface of the AlGaH2 system, utilizing DZP basis sets in conjunction with five correlated methods, the most highly-correlated being coupled-cluster theory including single, double, and perturbative triple excitations [CCSD(T)]. Equilibrium geometries, harmonic vibrational frequencies, dipole moments, and infrared intensities of a planar dibridged structure, two asymmetrical monobridged structures, two vinylidene-like structures, a trans structure, and a linear structure are presented. As anticipated the planar dibridged structure was the global minimum at all correlated levels of theory. The two monobridged minima were found to lie close in energy to the dibridged global minimum [within 9.8 kcal mol(-1) at DZP CCSD(T) including zero point vibrational corrections]. The theoretical results indicate that several of these isomers may be experimentally observable. The potential energy surface of AlGaH2 is found to be intriguingly related to those of Al2H2 and Ga2H2.