We have investigated the photoluminescence (PL) dynamics of excitons at the mini-Brillouin-zone edge (k(z)=pi/D), the so-called pi point, in a GaAs/AlAs superlattice (SL): D is a SL period. Under the resonant excitation condition of the first quantized (n = 1) heavy-hole (HH) exciton at the Gamma point (k(z)=0), it was found that the PL band of the n = 1HH exciton at the pi point is observed from time-resolved PL spectra. The temporal profile of the PL of the pi-point exciton exhibits a considerable delay time, similar to 40 ps, to that of the Gamma-point exciton and a very short decay time, similar to 12 ps. Note that the PL of the pi-point exciton has been never observed under off-resonant excitation of the Gamma-point exciton. The delay time is attributed to the transit time from the Gamma point to the pi point in the mini-Brillouin zone. The very short decay time results from that the pi point is a metastable state in the miniband dispersion. The mechanism of the transit process of the excitons is discussed from aspects of excitation-power dependence and scattering by folded longitudinal acoustic phonons peculiar to the SL. (c) 2013 Elsevier B.V. All rights reserved.