In this paper the classical kinetic theory of simple liquids developed by Born & Green is generalized for liquid mixtures. Though the fundamental equations preserve many of the general features of those relating to simple liquids, emphasis is laid on certain points characteristic of a liquid mixture. In the expansion procedure, improvement has been made in the choice of parameters; the potentials of the external force fields are taken as parameters instead of the external forces in order that force diffusion should follow naturally. The hydrodynamical equations for a liquid mixture follow after a set of relations between the observable quantities and those defined with respect to each component in the mixture have been obtained. These equations when compared with the corresponding ones for gas mixtures reveal the peculiar complicated features of liquid mixtures. A practical method of solution for the expanded equation of motion is discussed and general expressions for the coefficients of ordinary diffusion and thermal diffusion and also the coefficient of viscosity in a liquid mixture are given in the last section.