We present a ``transform'' theory for analyzing resonance Raman scattering under the condition of energy or state dependent dampibng. The energy dependence of the damping is taken to be linear in the Raman quantum but arbitrary in the remaining subspace of vibrations. The theory is tested using exact sum-over-states model calculations. The effects of truncation error are explicitly assessed. The method is applied to a Raman excitation profile of cytochrome P450, which is ``red shifted'' with respect to the resonant absorption band.