Results are presented of both linear optical transmission and femtosecond four-wave mixing measurements, on a II-VI semiconductor microcavity into which three quantum wells have been inserted. The excitons (Xs) confined in the wells are strongly coupled to the photons, and at resonance the transmission spectra reveal two polariton peaks of less than 2 meV width, and a Rabi splitting of 11.5 meV, demonstrating the high quality of the sample. The nonlinear emission shows strong and well-resolved beats at the Rabi frequency, that occur both for positive and negative time delays. These features are similar to those observed in a good-quality III-V microcavity. On the basis of a semiclassical Maxwell-Bloch model, they are attributed to the strong X-photon coupling causing oscillations in the X population during the coherent transient. The slightly longer decay time of the lower polariton branch observed at resonance is related to the dephasing properties of localised X states. (C) 1998 Elsevier Science B.V. All rights reserved.