We study theoretically the ultrafast nonlinear optical response of quantum well excitons in a perpendicular magnetic field. We show that for magnetoexcitons confined to the lowest Landau levels, the third-order four-wave-mixing (FWM) polarization is dominated by the exciton-exciton interaction effects. For repulsive interactions, we identify two regimes in the time evolution of the optical polarization characterized by exponential and power law decay of the FWM signal. We describe these regimes by deriving an analytical solution for the memory kernel of the two-exciton wave function in a strong magnetic field. For strong exciton-exciton interactions, the decay of the FWM signal is governed by an antibound resonance with an interaction-dependent decay rate. For weak interactions, the continuum of exciton-exciton scattering states leads to a long tail of the time-integrated FWM signal for negative time delays, which is described by the product of a power law and a logarithmic factor. By combining this analytic solution with numerical calculations, we study the crossover between the exponential and nonexponential regimes as a function of magnetic field. For attractive exciton-exciton interactions, we show that the time evolution of the FWM signal is dominated by biexcitonic effects. © 2000 The American Physical Society.