Systematic theoretical studies of the [XMYH](n) inorganic rings and clusters (M = Al, Ga, In; Y = N, P, As; X = H, F, Cl, Br, I; n = 1-6) have been carried out using hybrid Hartree-Fock density functional theory. A consistent set of the structural and thermodynamic properties has been obtained. The stability of the MY bond decreases in the order Al > Ga greater than or equal to In; N much greater than P > As. Terminal groups X have a minor influence on the subsequent elimination enthalpies of the clusters. In the case of X = H, hydrogen elimination makes formation of the [HMYH](6) oligomers from MH3 and YH3 thermodynamically favorable; while in the case of halide substituents, formation of [XMYH](6) is thermodynamically unfavorable, except for the system with the strongest MY bond (AIN). Substitution of the acidic hydrogen by X is favorable energetically for all [HMYH]6 clusters, but is complicated by the processes of cluster destruction to form the [X2MYH2](2) dimers. The high stability of the [HMNH](6) clusters makes them attractive single-source precursors for the production of 13-15 composites.