The role of non-adiabatic interactions in vibronically induced Raman scattering processes is examined for both the preresonance and resonance regimes. Attention is focused on the class of molecules whose linear electron-vibration coupling strengths are characteristic of the larger poly-atomic, e.g., the benzenoid azomatics. Various approximations are introduced to simplify the general theory and the applicability of each is discussed. It is shown that for randomly oriented scatterers the non-adiabatic contribution to induced scattering in the pre-resonance regime is of minor importance relative to the adiabatic contribution. For oriented scatterers, e.g., molecular crystals, some control over the non-adiabatic contribution can be achieved through choice of polarization conditions. For resonance Raman scattering it is shown that the non-adiabaticity can play an important role in vibronically induced scattering processes.