The single crystals of GaN were grown at a high pressure of 10-20 kbar and a high temperature of 1500-1800 degreesC. The crystals have the form of hexagonal platelets of size up to 100mm(2) and dislocation density smaller than 10(3)cm(-2). These crystals were used as substrates for epitaxy of III-N compounds. Measurements indicate that the crystallographic structure of the substrates is reproduced in the epi-layers of the ternary compounds. AlGaN and InGaN, of compositions and thicknesses used in most of the nitride-based devices. including a blue-laser structure. The very low dislocation density in these layers and their structures is documented by X-ray diffraction, atomic force microscopy and high-resolution transmission electron microscopy. The multiple quantum wells of InGaN/GaN have very sharp interfaces not disturbed by the presence of dislocations.