Comprehensive quantum chemical analysis with the use of the multireference state-averaged complete active space self-consistent field approach was carried out to study the reactions of H-2 with O-2 in a(1)Delta(g), b(1)Sigma(+)(g), c(1)Sigma(-)(u), and A(')3 Delta(u) electronically excited states. The energetically favorable reaction pathways and possible intersystem crossings have been revealed. The energy barriers were refined employing the extended multiconfiguration quasi-degenerate second-order perturbation theory. It has been shown that the interaction of O-2(a(1)Delta(g)) and O-2(A(')3 Delta(u)) with H-2 occurs through the H-abstraction process with relatively low activation barriers that resulted in the formation of the HO2 molecule in A '' and A' electronic states, respectively. Meanwhile, molecular oxygen in singlet sigma states (b(1)Sigma(+)(g) and c(1)Sigma(-)(u)) was proved to be nonreactive with respect to the molecular hydrogen. Appropriate rate constants for revealed reaction and quenching channels have been estimated using variational transition-state theory including corrections for the tunneling effect, possible nonadiabatic transitions, and anharmonicity of vibrations for transition states and reactants. It was demonstrated that the calculated reaction rate constant for the H-2 + O-2(a(1)Delta(g)) process is in reasonable agreement with known experimental data. The Arrhenius approximations for these processes have been proposed for the temperature range T = 300-3000 K.