We developed theoretically and experimentally the principles of a spectroscopical method based on resonance transient population gratings for quantitative description of solvation dynamics of large molecules in liquid solutions. The solvation dynamics of LDS 750 in N -monosubstituted amide, ethylacetamide and butylacetamide have been measured. This class of solvents exhibits exceptionally large static dielectric constants. The solvation dynamics of LDS 750 in all solvents consists of ultrafast as well as slow components. A theoretical basis for solvation dynamics study of complex molecules in solutions by resonance nonlinear spectroscopy has been developed. We have introduced a model of an optically active non-Markovian oscillator (NMO) for the description of solvation dynamics in nonlinear optical experiments in a systematic way. It has been shown that an optically active Brownian oscillator and different NMO models can be considered as successive long time approximations to a real correlation function of an optically active oscillator. The model of two NMOs with an exponential memory function describes accurately various experimental and computer simulations data of ultrafast solvation dynamics. We have compared the latter model with modern theories of solvation.