A stochastic theory of the spectral distribution of light scattered by mixtures of atoms and molecules, colliding in time and space, is proposed. New time-correlation functions C(0)(t) and C(2)(t) are introduced describing respectively the statistical microscopic mechanisms of isotropic and anisotropic coherent scattering, related with changes in the first and second perturbation of the molecular polarizability tensor due to the long-range fields of induced molecular electric multipoles. In this way, not only anisotropic but also isotropic scattering is shown to have a rotational spectral structure due to orientational motions and angular collisions of the polar molecules. The hitherto not considered cross approximations 0,1 and 0,2 of the functions C(0)(t) and C(2)(t) involve the first power of the dipole–quadrupole, dipole–octupole, and quadrupole–quadrupole tensors thus permitting first determinations of the signs of the successive multipolar molecular polarizabilities.