A technique that makes it possible to investigate the mechanisms of phase relaxation of excitons in GaAs single quantum wells has been developed using resonant reflection spectroscopy. The dependence of the oscillator strength of the exciton transition on the quantum well thickness has been measured in the thickness range 9.1-30.0 nm. It has been demonstrated that the oscillator strength with a high accuracy does not depend on the temperature in the range 8-90 K. The temperature dependence of the homogeneous broadening has been measured, and the inhomogeneous broadening of the resonance exciton line has been determined. A nonmonotonic dependence of the spectral broadening of the exciton line on the intensity of the resonant excitation at a temperature of 8 K has been revealed for the sample with a high-quality quantum well. It has been established that an increase in the excitation level by five orders of magnitude above the linear limit leads to an insignificant change in the oscillator strength of the excit