Epitaxial growth of GaN on beta-Ga2O3 single crystal substrates by the molecular beam epitaxy technique is demonstrated for the first time. Standard and in-plane X-ray diffraction evidence the growth of c-plane wurtzite GaN on a-plane beta-Ga2O3, the epitaxial relationship being < 010 >(Ga2O3)parallel to < 11 (2) over bar0 >(GaN) and < 001 >(Ga2O3)parallel to <(1) over bar 100 >(GaN). Epitaxial growth without any buffer layer is achieved after an effective surface nitridation under NH3 gas. (c) 2005 Elsevier B.V. All rights reserved.