The thermodynamic relationships for mixtures of nonmesomorphic compounds are applied to liquid crystalline materials. Equations developed for ascending solid solutions have been applied to mixtures of liquid crystalline materials. Computer programs, written to calculate the theoretical curves for such mixtures, are found to agree with the experimental data obtained for 4-alkyl and 4-alkoxy 4'-cyanobiphenyls and a series of p,p'-dialkoxyazoxybenzenes. The heats and temperatures of the transitions of the pure components, necessary for the theoretical calculations, were determined by polarized light microscopy and by differential thermal analysis. Polarized light microscopy was also used to determine the transition temperatures of the mixtures.