The theory of stimulated Rayleigh-wing scattering in anisotropic molecular liquids is discussed. This theory is extended to include liquid mixtures. When binary mixtures are considered, a singularity is found in the threshold condition in certain circumstances. This leads to the possibility of measuring the anisotropic polarizability difference for one of the liquids. In addition, the appearance of the singularity suggests a method of determining whether saturation plays an important role in stimulated Rayleigh-wing scattering.