High-quality ZnO epilayers have been grown on Zn-face ZnO substrates by plasma-assisted molecular beam epitaxy. With increasing O/Zn flux ratio from the stoichiometric to the O-rich, the growth mode changed from three- to two-dimensional growth and the line widths of (0 0 0 2) and (1 0 1 0) omega-rocking curves showed dramatic narrowing from 471 to 42 arcsec and from 163 5 to 46 arcsec, respectively. These values are narrower compared to those of ZnO on sapphire and also those of device-grade MOCVD-grown GaN. Moreover, A-, B-excitons (FEA, FEB), and the n = 2 state of FEA at 3.378, 3.393, and 3.424 eV, respectively, were clearly observed in the low-temperature (4.2 K) photoluminescence spectrum of ZnO grown under O-rich flux conditions. Our results show that growth under high O-rich flux conditions is required to produce high-quality Zn-polar ZnO films. (C) 2004 Elsevier B.V. All rights reserved.