In-situ and real-time monitoring on RF-MBE growth of GaN on sapphire substrate was carried out by using spectroscopic ellipsometry and reflection high-energy electron diffraction. Two relaxation processes were identified through the accompanying surface roughening in RF-MBE growth of GaN. The first relaxation of GaN on sapphire substrate happened through Stranski-Krastanov mode growth in the very initial stage of buffer. With further deposition, a smooth buffer layer was obtained and growth mode was changed to 2D. The second relaxation took place during the buffer layer temperature ramping process, and the relaxation temperature depended on the buffer layer growth temperature. After the second relaxation, the buffer layer became partly connected islands, as confirmed by AFM observation. These two relaxation processes were revealed to have important effects on epilayer quality. (C) 2002 Elsevier Science B.V. All rights reserved.