The electronic and geometric structures of gallium dinitride cation, GaN2+ and gallium tetranitride cation, GaN4+ were systematically studied by employing density functional theory (DFT-B3LYP) and perturbation theory (MP2, MP4) in conjunction with large basis sets, (aug-)cc-pVxZ, x = T, Q. A total of 7 structures for GaN2+ and 24 for GaN4+ were identified, corresponding to minima, transition states, and saddle points. We report geometries and dissociation energies for all the above structures as well as potential energy profiles, potential energy surfaces, and bonding mechanisms for some low-lying electronic states. The calculated dissociation energy (D-e) of the ground state of GaN2+, (X) over tilde (1)Sigma(+), is 5.6 kcal/mol with respect to Ga+(S-1) + N-2(X-1 Sigma(+)(g)) and that of the excited state, (a) over tilde (3)Pi, is 24.8 kcal/mol with respect to Ga+(P-3) + N-2(X-1 Sigma(+)(g)). The ground state and the first excited minimum of GaN4+ are of (1)A(1)(C-2 nu) and B-3(1)(C-2 nu) symmetry with corresponding D-e of 11.0 and 43.7 kcal/mol with respect to Ga+(S-1) + 2N(2)(X-1 Sigma(+)(g)) for X(1)A(1) and Ga+((3)p) + 2N(2)(X-1 Sigma(+)(g)) for B-3(1).