Due to the peculiarities of the growth process of GaN and related alloys on sapphire substrates, reflection high-energy electron diffraction (RHEED) is not sufficient to correctly monitor all the different steps of molecular beam epitaxy growth (MBE). It is shown that laser reflectivity, which is a very simple method, is highly complementary to RHEED. However, RHEED remains an unrivaled tool for the precise control of the growth. In particular, the observation of RHEED intensity oscillations can be used, as for classical semiconductors, to determine the growth rate with monolayer precision and also the composition of ternary alloys such as AlxGa1-xN. The accuracy of such a RHEED based control of MBE growth of nitrides is exemplified by the optical properties of GaN/AlxGa1-xN quantum well structures. (C) 1999 Elsevier Science B.V. All rights reserved.