We illustrate how interesting it is to use an elliptically polarized laser beam for the investigation of the polarization properties of dense excitonic systems in semiconductor quantum wells. We investigate the spectral splitting of the exciton luminescence, observed in GaAs multiple-quantum-well structures at high exciton density, when the polarization of the resonant laser beam is progressively varied from circular to linear: this method leads to the accurate determination of the strengths of both repulsive and attractive parts of the interaction between the excitons. We investigate the stability of the polarized excitonic phase as a function of both the ellipticity and the intensity of the photogenerating picosecond laser beam and measure the longitudinal and the transverse spin relaxation times on the same excitonic phase: the observations illustrate the driving role of the exciton – exciton exchange interaction in the spin relaxation mechanism at high density.