The effects of intermolecular vibrational coherence transfer on ultrashort time-resolved coherent anti-Stokes Raman scattering (CARS) from a molecular mixture are reviewed from a theoretical viewpoint. The coherence transfer is induced by the intermolecular interactions through a common heat-bath mode. The time evolution of the intermolecular coherence is reflected in the appearance of the quantum beats in the ultrashort time-resolved CARS spectra. When the structure of the molecular ensemble, for example, a multispherical-layer structure for the molecules in liquids, is taken into account, a slow decrease in the amplitudes of the beats appears in the case of long-range spatial coherence. We clarified how the coherence transfer is related to the modulation of the quantum beats in the time-resolved CARS spectra.