A theoretical and experimental study of the exciton in ultra-narrow quantum wells (QWs) is performed. A crossover from strong (separate localization of electron and hole levels) to weak confinement (with localization of excitonic center of mass) is predicted to occur for decreasing thickness, and is characterized by a minimum of the oscillator strength per unit area. Cathodoluminescence measurements performed on a series of GaAs/Al0.35Ga0.65As QWs with thicknesses from one to eight monolayers show a minimum of the oscillator strength, in agreement with theory, and indicate that the crossover from strong to weak confinement occurs at a thickness of about three monolayers for this composition. (C) 1998 Elsevier Science B.V. All rights reserved.