The initial stage of liquid phase heteroepitaxy (LPHE) of the III-V ternary alloys from the supercooled dilute liquid solutions, taking into account the lattice mismatch between the epitaxial layer and substrate, is considered. The non-equilibrium epitaxial process is described by the minimum condition of the Helmholtz free energy of the heterogeneous system. The affinities of formation reactions of the binary compounds constituting the III-V ternary alloys are equal to one another at the heteroepitaxial growth. The compositional dependencies of the InxGa1-xP alloys grown from the 10degreesC supercooled liquid solutions on the temperature are demonstrated. The lattice-pulling effect dominates at the initial stage of the LPHE of the lattice mismatch alloys from the supercooled liquid solutions. The theoretical estimations of the compositions obtained for the InxGa1-xP and GaAsxP1-x alloys are compared with the available experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.