The initial stage of growth of group III-Nitride ternary compounds on binary substrate were analysed using the classical nucleation theory, incorporating the stress induced supercooling due to lattice mismatch between the grown alloy and substrate. The explicit expression for the growth of the chosen system was established and it was used to evaluate the nucleation parameters. It has been theoretically shown that the nucleation barrier for the formation of ternary alloy on binary substrate depends on the composition of the alloy.