on the occasion of his 80th birthdayThe nonlinear response of a dense exciton gas in a platelet on an externally driven field is discussed using non equilibrium Green's function technique. A generaliz,ed Boltzmann-equation of excitons containing many-particle corrections in the diffusion-, drift-and collision-term is derived. Using a relaxed distribution (Boltzmann-distribution) and an unrelaxed distribution (macro-occupation) of Is-excitons a bistability in exciton density as well as in the transmitted light intensity is obtained for a nearly resonant and stationary applied pump-field of intensity 0.1 and 10 kW/cm2, respectively. The bistability is obtained as a pure excitonic effect below the Mott-transition.