In this work we have analysed the conditions to grow epitaxial layers by Liquid Phase Epitaxy (LPE) from ternary Ga-As-P liquid phases on GaAs and GaP under initial conditions that are far away of the thermodynamic equilibrium. First, it is shown that the liquid-solid (L-S) interfaces are “stable” for all compositions of the liquid phases exclusively in contact with the GaP substrates. At the same time the elastic energy generated in mismatched GaAsyP1-y layers induces a reduction in the As content of the layer. Then, it should be expected that highly lattice mismatched epitaxial layers could be grown with small elastic energy, so that beyond certain stress the layers are initially non-planar having spatially separated but simultaneous local centres of nucleation and dissolution pits. These processes should cause a change on the composition of the liquid phase and, as consequence, the formation of the epitaxial islands with a composition gradient along its thickness. Our estimations show that in the case of contact of a Ga-As liquid phase with a GaP substrate the P content in the epitaxial islands increases with its thickness. The thermodynamic analysis was done with the CALPHAD method using SGTE data.