We report the results of a photoluminescence excitation (PLE) study on excitonic transitions in GaN. PLE measurements were carried out as a function of temperature to investigate exciton formation, thermalization, and annihilation processes in GaN. The PLE spectra detected at free-exciton resonance were found to exhibit a large number of oscillatory emission structures with an energy spacing of LO-phonon (92 meV), and such emission persisted up to 400K. The observation suggests that a phonon-assisted indirect exciton formation process, which simultaneously generates a free-exciton and an LO-phonon, is very significant and efficient in GaN, and the lifetime of the free-exciton is longer than the relaxation time of LO-phonon emission but much shorter than that of acoustic-phonon emission. The appearance of the broad spectral features at the PLE spectrum detected at free-exciton resonance, similar to those measured at the boundexciton resonance, is attributed to the higher order transition processes which involve acousticphonon scattering and thermal repopulation of free-excitons. In addition, we observed up to the 12th LO-phonon emission in PLE spectrum around 120 K, indicating the existence of the excitons with a large kinetic energy in GaN.