Resonance enhanced stimulated Raman scattering (RESRS) from the ground X (1) Sigma(g)(+) (upsilon(g) = 0, J(g) = 0-2) state of a H-2 molecule via intermediate B (1) Sigma(u)(+) (upsilon(i) = 14, J(i) = 0-3) and (1) Pi(u) (upsilon(i) = 3, J(i) = 1-3) states coupled nonadiabatically with each other is studied theoretically in the presence of laser and Stokes fields applying the second-order perturbation technique. The present study includes the calculation of Raman gain (g(R)) of Stokes intensity resulting from various Q- and S-branch transitions considering the parallel-parallel, parallel-perpendicular, and circular (both same and opposite senses) polarizations of the laser and Stokes beams. The g(R) profiles are investigated for the ranges of incident photon frequency (<(nu)over bar>(L)) about the resonance values [<(nu)over bar>((res)(L))] for the two perturbed vibronic states (B,C). For the frequencies considered both the large resonance enhancement and the polarization dependence of the stimulated Raman gain spectra can be computed by taking into account the resonant intermediate levels only. In general, the Franck-Condon vibrational overlap and the configuration coupling determine the gain. The angular parts of transition matrix elements determine the polarization effect for the specified range of <(nu)over bar>(L) and a particular set of rotational-vibrational quantum numbers. For Q-branch transitions, in most of the cases, the maximum and minimum gains occur, respectively, for the same- and opposite-sense circular polarizations of two fields while for S-branch transitions the results are reversed. The calculated g(R) values for RESRS in some cases are found to be larger by about ten orders of magnitude than the values obtained for nonresonant stimulated Raman scattering in H-2. The variation of g(R) with gas temperature at constant density is also studied in some specific causes using the thermal Boltzmann distribution for vibrational-rotational states at different temperatures and polarizations. This study indicates that the thermal dependence of RESRS gain is different for different cases of transitions depending on the polarizations of the laser and Stokes lights. (C) 1997 American Institute of Physics.