We present an experimental and theoretical study of the dephasing of heavy-hole excitons in a 70- GaAs/AlxGa1-xAs multiple-quantum-well stucture. We measure the time-integrated three-pulse four-wave-mixing signal of heavy-hole excitons in the quantum-well sample. We model the third-order nonlinear optical response incorporating the effects of a stochastic modulation of the transition frequency. We find that the dephasing of the nonlinear polarization is mainly the result of a spectral-migration process of the excitons and, to a lesser extent, due to a homogeneous dephasing process. The time dependence of the four-wave-mixing signal is very well described by theory if the spectral-migration process is assumed to be energy dependent.