A comparative study of epitaxy of AlN, GaN and their alloys, grown on c-axis and off-axis substrates of single-crystal aluminum nitride has been carried out. Growth on off-axis (> 30degrees) substrates appears to result in rough surfaces and the absence of two-dimensional electron gas (2DEG). However, smooth morphologies were demonstrated for both homoepitaxial and heteroepitaxial growth on on-axis (< 2degrees) substrates, On one of these oriented substrates a 2DEG, with a mobility of 1000 cm(2) Vs and a sheet density of 8.5 x 10(12) cm(-2) at room temperature, was also demonstrated for the first time. (C) 2002 Elsevier Science B.V. All rights reserved.