A study is reported of the influence of saturation of the dipole moment of an exciton transition on transient transmission of an ultrashort laser pulse by a semiconductor film in the exciton spectral range. A threshold is predicted at which the transmission changes from total reflection by a film to total bleaching of the film, as the rate of excitation is increased. An analogue of the McCall - Hahn area theorem is derived for ultrashort pulses interacting with a film. When the nonlinear parameter is large, the dependence of the area of a pulse transmitted by a film on the area of an incident pulse becomes multivalued.