We have studied the growth and characterization of ZnO epilayers on GaN templates by plasma-assisted molecular beam epitaxy. Pregrowth treatments of the GaN surface by using Zn or oxygen plasma exposures result in different growth processes as indicated by the evolution of a reflection high-energy electron diffraction (RHEED) pattern. The Zn pretreatment provides a well-ordered GaN surface for ZnO epitaxy, while the oxygen plasma pretreatment reveals the formation of a disordered surface. Investigation on a ZnO/GaN interface by high-resolution transmission electron microscopy shows that a Ga2O3 interface layer is formed at the ZnO/GaN interface by oxygen pretreatement, which results in degradation of crystallinity of ZnO epilayers. In order to accommodate lattice strain and interface mismatch, a low-temperature ZnO buffer layer with a thickness above the critical thickness for strain relaxation is deposited on the GaN surface. The surface of the low-temperature ZnO buffer layer becomes atomically smooth by the following high-temperature annealing, which enhances two-dimensional growth of ZnO. The two-dimensional growth from the very beginning of epitaxy on a ZnO buffer layer is confirmed by RHEED intensity oscillation. X-Ray diffraction curves of ZnO layers on various reciprocal spots with different scans, are discussed in terms of strain and threading dislocation in the layers. It is concluded that the structural quality of the ZnO epilayer is limited by the quality of the GaN template. Photoluminescence spectrum of a typical ZnO epilayer under a weak excitation condition is dominated by excitonic emission with bound exciton emission being dominant below 77 K, while the free exciton emission becomes strongest above 77 K. When a ZnO epilayer is highly excited at 77 K, the free exciton emission is overtaken by biexciton emission at an excitation intensity of approximately 10 W/cm(2). The observation of the biexciton emission will help develop novel non-linear optical devices based on large optical oscillator strength in the biexciton process.