One of the significant problems of molecular spectroscopy is the determination and detailed analysis of how molecular vibrations are dephased. The dephasing of infrared-active (IR-active) vibrations of molecules was investigated by IR absorption spectroscopy. Pulse methods were used to investigate IR-vibrations as well. These methods revealed such coherent nonstationary effects as optical nutation, damping of the free polarization, photon echo, etc. New means of studying dephasing processes were uncovered by the method of nonstationary (time-domain) coherent anti-Stokes Raman scattering (CARS) spectroscopy. However, there are some aspects of CARS that still are not fully covered. One of them is related to Raman scattering by polaritons in dipole-active crystals whereas the second one is the increase of efficiency of CARS (minimization of the wave mismatch, the relationship between pulse width and the relaxation time, etc.). The purpose of the present research to study the case of "extreme" coherency between all interacting pulses (the duration of each pulse is smaller than characteristic times and those pulses are traveling with the same speed) in dipole-active crystals. In this research, we analyzed the process of simultaneous propagation of three waves (anti-Stokes, Stokes, and the pump) under CARS by polaritons. We have found some solutions modeling such simultaneous propagation. We also found the expression for the gain factor for such scattering. The gain factor was evaluated under the assumption of a given stationary pump field. It was shown that the typical values of the relative intensities were consistent with the experimental results.