The stability of a nematic phase in binary mixtures of Liquid crystals (LC) with non-nematogenic solvents, was analyzed using the combined Flory-Huggins and Maier-Saupe models. Stability was described using general criteria developed by Dorgan [Liq. Crys. 10, 347 (1991)], applied to the g(phi(1),s) function describing the free energy density of the system (phi(1)=volume fraction of LC, s=orientational order parameter). Equivalent criteria were obtained by replacing s by the particular s(phi(1)) function that minimizes g and making d(2)g[phi(1),s(phi(1))]/d phi(1)(2)>0, to define stability. Recent results reported by Shen and Kyu [J. Chem. Phys. 102, 556 (1995)] were reanalyzed using general stability criteria. It was found that the spinodal curve for the nematic phase extended beyond the limit fixed by these authors. In particular, the spinodal enters the region where the isotropic phase is the stable one, in agreement with other calculations reported by Dorgan for a nematic phase described by a modified Flory-Ronca model. A pure LC may exist in a metastable state in a small temperature range located above T-NI (equilibrium temperature of the nematic to isotropic transition of the pure LC).