The robustness of AlGaAs/GaAs quantum well to strong resonant excitation is studied. It was found that lowering Al concentration in barriers to 3% does not influence the measured radiative linewidth of exciton resonance in the sample at low intensities. At the same time parasitic broadening of the resonance by an additional resonant illumination is strongly suppressed as compared to the quantum well with 30% of Al in barriers.