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Summary form only given. When a quantum-well exciton transition is resonant with a single mode of a high-Q microcavity the linear reponse of the coupled system may be described in terms of normal modes ("cavity polaritons"), which arise as a result of the interplay of absorption and dispersion of the exciton transition within the cavity. The nonlinear response of these systems has often been discussed in terms of "polaritonic nonlinearities". It is desirable to investigate the nonlinearities of normal-mode microcavities (NMC's) at the same level and to determine if the microscopic theory accounting for the bare-QW response also quantitatively accounts for the normal-mode nonlinear response. We report here an extensive series of pump-probe experiments, investigating the time-resolved reflectivity of an NMC as a function of pump and probe polarization and pump fluence.