We consider the presence of instability domains in the phase diagram of epitaxial solid solutions of ternary and quaternary III-V compounds. We first study the elastic energy term in the Gibbs free energy of a strained epitaxial layer and we give the magnitude of this term for the III-V binary compounds. We then examine ternary compounds and we show that strains induced by a substrate make stable the materials which would be expected unstable in the regular solution model. We finally apply to quaternary compounds a stability criterion based on the total. curvature of the surface describing the free energy as a function of composition. Here again, the epitaxy of an unstable solid solution on a lattice-matched substrate makes it at least metastable