We proposed a heteroepitaxial lateral overgrowth technique using periodically grooved substrates to prepare a GaN single crystal with low dislocation density. By this technique, GaN single crystals have been grown without a selective growth mask or GaN single crystal seeds. Moreover, the AlGaN single crystal, which is important for optoelectronic devices in the UV region, can also he grown using this technique. The reduction of the threading dislocation density in AlxGa1-xN single crystals grown on periodically grooved substrates was confirmed by transmission electron microscopy. (C) 2002 Elsevier Science B.V. All rights reserved.