  We present a systematic study on the exciton relaxation in high purity AlGaAs
epilayers. The time for the excitonic photoluminescence to reach its maximum
intensity (t_max) shows a non-monotonic dependence on excitation density which
is attributed to a competition between exciton localization and carrier-carrier
scattering. A phenomenological four level model fully describes the influence
of exciton localization on t_max. This localization effect is enhanced by the
increase of the Al content in the alloy and disappears when localization is
hindered by rising the lattice temperature above the exciton trapping energy.
