A general microscopic theory of viscoelasticity for a binary mixture of two species is developed by using projection operator formalism. The theory is applicable to binary polymer blends, binary mixtures of nonpolymeric fluids, and solutions of homopolymers in a solvent of small molecules. Particular attention is given to the effect of viscoelasticity on the spectrum of quasi-elastic light (QEL) scattering from semidilute and concentrated polymer solutions. The results are compared with those previously obtained by Wang using the linearized hydrodynamic description of binary fluids which predict that the viscoelastic effect on the QEL spectrum will vanish when the specific volumes of the polymer and the solvent molecules are equal. We find that there is an additional contribution to the viscosity, not present in Wang’s theory, that can account for the viscoelastic effect experimentally observed by Brown and Stepanek in semidilute solutions near theta condition even when the specific volumes are matched.