We report frequency-domain degenerate four-wave mixing results on exci
tons in a semiconductor microcavity in the strong coupling regime. The
excitation is kept to the chi((3)) limit. The spectral response shows
strong polarization dependence. We analyze the data with a new model
where the degenerate four-wave mixing process is described as an elast
ic scattering of two cavity polaritons mediated by the state filling e
ffect and the two-body attractive and repulsive interaction between ex
citons. From the polarization and detuning dependence, the ratio of th
e coupling constants of these three terms is uniquely determined. We f
ind that the attractive interaction term and the state filling are the
dominant contributions to the nonlinearity.