The process of nucleation and subsequent evolution of GaN on the substrate surface covered with a buffer layer was investigated theoretically. The rates of nuclei flows and the size distribution functions for the islands formed at substrate temperatures T > 480 °C were calculated for substrates covered with AlN buffer layers. All the major mechanisms of island growth were considered. It has been shown that at a temperature of T = 480 °C islands of liquid Ga are first formed. Next, chemical reactions between gallium and nitrogen with formation of GaN take place on the substrate surface. At 750 °C > T ≥ °C, only GaN is nucleated. The Ostwald ripening process in an ensemble of GaN islands was studied and a phase diagram of such an ensemble constructed.