Raman scattering of molecular oxygen in the region of the Schumann-Runge absorption band system is calculated from first principles in the second order of perturbation theory in the interaction of photon-electron operator. Quantitative predictions are given for the cross sections for scattering of photons and a detailed comparison is made with available measurements. The behavior of Raman spectra near the predissociating rovibronic level (upsilon' = 5,N') in the B (3) Sigma(u)(-) electronic State of O-2 is investigated and shown to have significant dependence on the detuning of the incident laser frequency. By casting the Raman transition matrix in a form similar to the Fano formalism, we are able to investigate the nature of the resonant and nonresonant scattering in the language of configuration interaction. By varying the predissociating width of the (upsilon' = 5,N') resonance, we make a comparison with an earlier time-dependent wave-packet analysis. We also calculate the depolarization ratio of the scattered photons parallel and perpendicular to the polarization of the incident laser beam for the different Raman branches for lines terminating in the v '' = 1 and v '' = 6 levels and comment on the relationship between resonant Raman scattering and fluorescence emission. (C) 1997 American Institute of Physics.