The electronic and geometric structures of gallium dinitride GaN2, and gallium tetranitride molecules, GaN4, were systematically studied by employing density functional theory and perturbation theory (MP2, MP4) in conjunction with the aug-cc-pVTZ basis set. In addition, for the ground-state of GaN4 (B-2(1)) a density functional theory study was carried out combining different functionals with different basis sets. A total of 7 minima have been identified for GaN2, while 37 structures were identified for GaN4 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 of GaN4. The dissociation energy of the ground-state GaN2 ((X) over tilde (2)Pi) is 1.1 kcal/mol with respect to Ga(P-2) + N-2(X-1 Sigma(+)(g)). The ground-state and the first two excited minima of GaN4 are of B-2(1) (C-2 nu), (2)A(1) (C-2 nu, five member ring), and (4)Sigma(-)(g)(D-infinity h) symmetry, respectively. The dissociation energy (D-e) of the ground-state of GaN4, (X) over tilde B-2(1), with respect to Ga(P-2) + 2 N-2(X-1 Sigma(+)(g)), is 2.4 kcal/mol, whereas the D-e of (4)Sigma(-)(g) with respect to Ga(P-2) + 2 N-2(X-1 Sigma(+)(g)) is 17.6 kcal/mol.