Nucleation kinetics during the Liquid-Phase Epitaxial (LPE) growth of In1_ x GaxP on GaAs substrate have been studied. The behaviour of non-equilibrium solid-liquid interface between In-Ga-P solution and GaAs substrate has been analysed and hence the expression derived for the stress-induced supercooling has been incorporated in the classical heterogeneous nucleation theory. The condition for the growth of good-quality GaInP layer on GaAs substrate has been shown theoretically.PACS 68.55.Df-Liquid phase epitaxy.