The spin-orbit coupling constants (A(v+)) for O-2(+)(A (2)Pi (u),v(+)=0-17) and O-2(+)(a (4)Pi (u),v(+)=0-25) were computed based on the Pauli-Breit Hamiltonian with one and two electron terms for comparison with experimental measurements. In the present theoretical study, the vibrational wave functions are obtained using the potential energy curve calculated at the multireference configuration interaction (MRCI) level of theory, with single and double excitations from the complete active space self-consistent field (CASSCF) reference wave function. The electronic wave functions and spin-orbit coupling constants are obtained at the CASSCF and restricted MRCI levels. The effect on A(v+) for O-2(+)(A (2)Pi (u),v(+)) and O-2(+)(a (4)Pi (u),v(+)) due to interactions of the O-2(+)(A (2)Pi (u),v(+)), O-2(+)(a (4)Pi (u),v(+)), and O-2(+)((2)Sigma (+)(u)) states is examined. The theoretical A(v+) predictions for O-2(+)(A (2)Pi (u),v(+)) are found to be consistent with the experimental finding that O-2(+)(A (2)Pi (u)) is an inverted spin-orbit state at low v(+) levels and becomes a regular spin-orbit state at higher v(+) levels. Good accord between theoretical predictions and experimental results for O-2(+)(A (2)Pi (u),v(+)=0-12) is observed with discrepancies in the range of 2-10 cm(-1). In the case of O-2(+)(a (4)Pi (u),v(+)), excellent agreement between theoretical ab initio and experimental results is found with a discrepancy of 2-5 cm(-1). Our effort to theoretically reproduce experimental fine structure in the A(v+) curve for O-2(+)(a (4)Pi (u),v(+)) based on interstate vibrational interactions has met with limited success.