The bleaching of the n = 1 and n = 2 heavy-hole exciton absorption has been observed at room temperature in ternary alloy Al0.37Ga0.63As/AlAs multiple-quantum-well structures by nanoseconds pump-and-probe spectroscopy. The relative variation of the absorption coefficient [(-DELTA-alpha)/alpha-0] are about 15% and 8%, respectively. The nonlinear absorption coefficient (alpha-2) and the nonlinear absorption cross section has been deduced. The value of the saturation density deduced from our spectra is in good agreement with the theoretical predictions. The influence of the staggered band alignment on the observed process is also discussed.