We studied the near-band-edge emission (NBE) and yellow defect luminescence (YL) of GaN under below bandgap excitation with 40-fs laser pulses at a wavelength of 775 nm. Even though in this case three-photon absorption processes are required for the excitation of band-to-band transitions, fourth-order (I_NBE ∝ I_exc⁴) and sub-linear (I_YL ∝ I_exc^0.5) dependencies were observed for the intensity of the NBE and YL as a function of the excitation intensity, respectively. Modelling the carrier dynamics with a few-level rate-equation model revealed that, for high excitation irradiances, the electron-hole population generated by three-photon absorption is such that the NBE recombination rate is intensified (exponent > 3) and, at the same time, the competition between the electron capturing and the defect-level emission rate suppresses the YL (exponent < 1).