An extension of the Brownian oscillator model in nonlinear optical spectroscopy to include frictional memory is treated. Although we have obtained analytic expressions for this model, their unwieldiness makes the understanding of the effect of nonzero frictional memory difficult. However, by focusing on the behavior of the analytically continued oscillator coordinate correlation function in the complex frequency plane, qualitative insight is obtained. Applications to spontaneous Raman scattering and two time-resolved coherent Raman scattering spectroscopies are briefly explored.