The 1-2 2Π1/2, 1-2 2Π3/2, and 1-3 2Σ1/2+ states of GaAr and the 1 1Σ+ and 1 3Σ− states of GaAr+ are calculated by ab initio methods. Spectroscopic properties for these states are compared with experimental data, and the existence of potential barrier for the Rydberg Σ1/22 states is explained. We have also proved the nonbonding character of the 1 2Π1/2(X) state of GaAr. The bond energy of the doubly excited 1 3Σ− state, 12 557 cm−1, is much larger than that of the ground state (X 1Σ+) of GaAr+, 584 cm−1, which in turn is more strongly bound than the neutral species (70 cm−1 for the ground state, 340 cm−1 for the 2 2Π3/2 state). The nonbonding character of the X 2Π1/2 state of GaAr can be attributed to the spin–orbit interaction. Transition properties between these states are also calculated.