The Maier-Saupe theory of the nematic mesophase is extended to multicomponent systems containing axially symmetric molecules interacting with a general anisotropic intermolecular potential. Expressions are derived for the anisotropic pseudo-potential of each component as well as the orientational molar Helmholtz function for the mixture. Simplified forms of these formulae are then employed, with some success, to predict the phase diagrams for two binary mixtures of nematogens. The possible application of the theory to interpret the solute activity coefficients determined by gas-liquid chromatography using a nematogen as the stationary phase is indicated.