We report on high-resolution X-ray diffraction studies of crystalline perfection and relaxation of elastic strain in GaN and AlN layers grown on SiC and sapphire substrates. Thin (300-500 nm) GaN layers are grown with a threading screw dislocation density of about 1-2 x 10(7) cm(-2). A density of 1.75-8.5 x 10(5) cm(-2), the lowest value ever reported for III-nitride epitaxial layers, is observed in thin (200-300 nm) AlN layers. In both cases, low density is observed in a surface layer formed over the defective nucleation layer. A model of spatial distribution of crystalline defects, based on generation of point defects on the growth surface, diffusion and further structural transformation under the action of volumetric elastic strain accounts for these observations. Perfect thin layers may be used as templates for epitaxial growth of perfect layers of other compositions, for example, GaN or InGaN layers for photovoltaic applications. (c) 2006 Elsevier B.V. All rights reserved.