The inventive method exploits the fact that in solutions or melts which contain certain organic substances, small nitride crystallites consisting of GaN or AlN are formed by thermal reaction and decomposition. A vessel containing the melt is kept at a first temperature T.sub.1. In the vessel is a substrate nucleus of be nitride to be formed, which is heated to second temperature T.sub.2 through the input of energy, where T.sub.2>T.sub.1. Epitaxial growth from the melt then takes place on the surface of the substrate nucleus. The energy input can be carried out in different ways.