We report time-resolved spectroscopy on exciton luminescence in low-di
mensional systems. The reduction of dimensionality from two in quantum
wells to one in corrugated superlattices can completely change the in
itial relaxation process. In the one-dimensional system exciton-phonon
scattering is, even at high exciton densities, faster than exciton-ex
citon scattering since the latter is reduced whereas the former is enh
anced if the final state falls into the singularity in the density of
one-dimensional states.