Summary form only given. The role of exciton-exciton scattering in the nonlinear optical response of semiconductor quantum wells is well established. However, an interesting question arising from the system's dimensionality has so far not been addressed. In the quantum theory of scattering in two dimensions, the scattering amplitude behaves non-smoothly and non-perturbatively at low energies. While the exact scattering amplitude vanishes as 1/ln (energy) as energy ↘0, the second Born approximation diverges logarithmically. These properties result from the system's dimensionality and hold for any short-range well-behaved potential. One may ask whether the second Born approximation also fails for exciton-exciton scattering in two-dimensional structures and how this breakdown may be experimentally detected. In this contribution, we address this question within a microscopic theory of frequency-degenerate four-wave-mixing signals from a quantum-well microcavity. Analyzing an experiment reported in with this theory, we argue that the data are already sufficiently sensitive to show the breakdown of the second Born approximation for exciton-exciton scattering.