Time resolved photoluminescence spectroscopy has been used to study the dynamics of the free and donor bound exciton transitions in GaN epitaxial layers grown by metal organic chemical vapor deposition (MOCVD). Luminescence spectra, recombination lifetimes of these transitions as well as their temperature dependencies have been measured, from which the radiative recombination lifetimes of about 0.12 ns for the neutral donor bound excitons and of about 0.4 ns for the free excitons have been obtained. The observed high radiative recombination rates of these transitions imply superior optical properties of the GaN, which promise many important optical device applications including efficient and fast UV-bule lasers based on GaN.