We investigate the mechanisms leading to the optical non-linearities observed on a strongly excited semiconductor microcavity containing quantum wells. This study of a coupled exciton-cavity system is possible owing to the availability of a sample of exceptionally high quality, permitting to exclude effects of disorder and inhomogeneous broadening. Sub-picosecond pump and probe experiments are performed, in the regime of an incoherent exciton gas of high density. For such a gas the dephasing due to collisions is not efficient enough to cause the break-down of the strong coupling and hence the collapse of the Rabi splitting. Phase-space filling and exchange effects are the dominant mechanisms. (C) 1999 Elsevier Science B.V. All rights reserved.