In this paper, a model describing the vector interaction of an intense backward-propagating Raman pump and a weak forward-propagating Stokes signal in randomly birefringent fibers is proposed. The model accounts for the losses, the Raman interaction, and the linear and nonlinear birefringence. Realistic characteristics of the backward-propagation-birefringence vector have been originally accounted for. Numerical solutions show that polarized-backward-Raman amplifiers can have gain fluctuations larger than previously reported because of linear- and nonlinear-birefringence effects. Moreover, the gain mean depends on the signal and pump state of polarization imposed at the amplifier input or output. Simple formulas are derived for predicting the gain mean when nonlinear effects can be neglected