Аннотация:The theoretical description for the build-up process of the nonlinear optical response is carried out in the case when the durations of used light pulses are comparable with the time of dephasing the electron excitation of a molecule. For the problem of the nonstationary resonance coherent antiStokes Raman scattering, the calculation of the nonlinear susceptibility is performed within the density matrix formalism. The perspectives of two experimental schemes of the resonance active spectroscopy in studying the relaxation processes in an excited electron state are discussed. The simple model for describing the evolution of the wavepacket in an excited electron state is developed. On the basis of the model the calculation of the depolarization ratio at the antiStokes frequency is performed.