Finite temperature model expressions for the excitation profiles of second-order Stokes resonance Raman (RR) scattering are derived within the framework of the time correlator theory for systems with simultaneous linear electron-phonon coupling and linear non-Condon coupling. These expressions have all the advantages common to solutions from the time correlator theory, allowing convenient and efficient multimode modeling procedures. These results, together with those obtained elsewhere for the second-order profiles of systems within the Condon approximation, but having mode mixing and frequency shifts, are applied to the RR scattering originating from the 700 nm absorption band of azulene. For this system, it was shown previously that the measured optical absorption and fundamental RR profiles cannot discriminate between a mode mixing model, invoked to account for the measured relative intensities of the fundamental profiles of two modes, and an equally successful non-Condon model; nor can recent quantum-chemistry calculations by others for this system. With our new model expressions for the second-order profiles, we calculate here the profiles of the combination/overtone bands involving these two modes, using either the same mode mixing model parameters, or the same non-Condon model parameters which were previously successful for the absorption and fundamental profiles. Our results show that the second-order profiles predict a clear discrimination between the two models. © 1990 American Institute of Physics.