The theory of nonstationary transmission of two supershort pulses of laser radiation by thin semiconductor film is developed. One of the incident pulses is in the resonance with two–photon transition from ground state of the crystal to the biexciton state, whereas the other pulse mixes coherently the exciton and biexciton states, resulting in a strong renormalization of energetic spectrum of the crystal. We have obtained the system of nonlinear equations describing the time evolution of the exciton and biexciton amplitudes and the fields of three transmitted through film pulses. We investigated the influence of amplitudes and widths of incident pulses and the time delay between them on the film transmittivity. We predicted the effect of a strong delay in transmitted by the film pulses relative to the incident one, which is in the resonance with the frequency of exciton–biexciton transition. We proved also the possibility of generation of precursor, which is the pulse transmitted by film earlier than the peak of incident pulse arrives the film