It is demonstrated by in situ reflection high-energy electron diffraction (RHEED) studies that the growth of cubic GaN on MgO occurs in a layer-by-layer mode under Ga-rich conditions, growth rates 0.25-0.30 ML/s and 700 degrees C substrate temperature. From streak-spacing analysis of the observed RHEED patterns, it is possible to infer that the GaN layer grows pseudomorphically on MgO up to 3 monolayers (ML). After that, a relaxation process begins and the layer-by-layer or 2-dimensional growth changes to a columnar or 3-dimensional growth, as evidenced by the transformation of the RHEED patterns, which change from streaky to spotty. The experimental critical thickness (h(c)) value of 3 ML is close to the prediction of the Frank-van der Merwe classical model of 2.5 ML Other models predict h(c) values 3-6 times the experimental value experimentally observed. (C) 2008 Elsevier B.V. All rights reserved.