study is reported of the influence of the saturation of the dipole momentum of an exciton transition on transient transmission of ultrashort laser pulses by a thin semiconductor film in the exciton range of spectrum. It is shown that when rectangular pulses of resonant laser radiation are incident on the film, a threshold-type qualitative change in the transmission by the film takes place from almost total reflection at low level of excitation to complete bleaching at high values of the incident pulse amplitude. An analog of the McCall-Hahn area theorem is derived for ultrashort pulses interacting with the film. When the nonlinear parameter is large, the dependence of the area of a pulse transmitted by the film on the area of an incident pulse becomes multivalued.