High-quality ZnO epilayers have been grown on Zn-polar 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 (0002) and (10-10) omega-rocking curves showed dramatic narrowing from 471 to 42 arsec and from 1635 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 WILEY-VCH Veriag GmbH & Co. KGaA, Weinheim.