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We report time-resolved spectroscopy on exciton luminescence in low-dimensional systems. The reduction of dimensionality from two in quantum wells to one in corrugated superlattices can completely change the initial relaxation process. In the one-dimensional system exciton-phonon scattering is, even at high exciton densities, faster than exciton-exciton scattering since the latter is reduced whereas the former is enhanced if the 6nal state falls into the singularity in the density of one-dimensional states.Fabrication of one-dimensional (1D) semiconductor quantum-wire structures is intriguing since peculiar physical properties, as, e. g., strong optical nonlinearity, high carrier mobility, ' large exciton binding energy, density of states with a strong singularity, and reduced carriercarrier scattering rate ' are expected in these lowdimensional systems. Some of these theoretically predicted properties have been experimentally verified: for example, Nagamune et al. demonstrated an anisotropic shrinkage of excitons and Oestreich et al. demonstrated that the exciton-exciton scattering rate in a quantum wire is reduced. Other properties of 1D systems still need to be experimentally demonstrated.Investigation of this one-dimensional physics depends critically on the successful fabrication of quantum-wire structures. The main problem is to fabricate such small structures that the spacing between quantized states is 1arge enough that efFects of reduced dimensionality can be clearly observed. Recently, an approach toward the synthesization of quasi-1D structures has been achieved by growing corrugated superlattices (CSL}. ' The basic concept is the in situ formation of an array of macrosteps during the molecular-beam epitaxy growth on high-index-oriented GaAs substrates.The structures have small wire dimensions with width and thickness of typically 5 nm. Various 1D effects like, e. g., an increased exciton binding energy and a pronounced optical anisotropy, have been demonstrated in these CSL structures. ' The structures have clear advantages with respect to wires fabricated in conventional ways: The wires of CSL's are very thin (4.3 nm), closely packed (with a distance of about 3.2 nm), and they have no free surfaces.Therefore, large quantization energies, large optical signals, and negligible nonradiative surface recombination are obtained with CSL's. Using these CSL structures we demonstrate in this paper how the initial relaxation process of hot excitons created by photons of a short laser pulse changes completely if the dimension of the system is reduced from 2D to 1D: In two dimensions, exciton-exciton or exciton-free-carrier scattering is at a moderate excitation density of 10' cm, by far the fastest initial process. In particular, it is faster than the optical phonon emission rate: no phonon replicas are observable in the emission of free excitons in GaAs quantum wells. In one dimension, the situation is different for two reasons: (i) exciton-exciton scattering is strongly reduced in a 1D dispersion and (ii} th...