A three-pulse degenerate four-wave-mixing experiment and its theoretical analysis reveal contributions of local field and biexciton effects to the nonlinear optical response of the two-dimensional exciton. Quantum beats with a frequency equivalent to the biexciton binding energy appear only for specific polarizations. Polarization-dependent spectrally resolved four-wave mixing shows an additional peak that is separated from the 1s heavy-hole exciton line by the biexciton binding energy. These experimental results are in good agreement with the optical selection rules of the theoretical model, providing evidence for biexcitonic contributions to the four-wave mixing.