We have investigated the interband recombination of dense two-dimensional (2D) electron gases in one-sided modulation-doped InxGa1-xAs and GaAs asymmetric single quantum wells, under a near-resonance condition between an exciton level from a higher electronic subband and the Fermi level. Under such conditions, the excitonic resonant enhancement of the Fermi-edge singularity is clearly identified in both systems. The optical oscillator strength of the electrons at the Fermi level recombining with photoholes is enhanced by over two orders of magnitude through the resonant coupling with the exciton state. The strength and character of the interaction of the exciton with the 2D electron gas ( 0.6 meV) is determined by photoluminescence spectroscopy, including its dependence on temperature and an in-plane magnetic field. In a perpendicular magnetic field, the periodic modulation in the formation of such coupled many-electron excitons leads to very large B-1-periodic intensity oscillations in the photoluminescence. © 1992 The American Physical Society.