Taking into account the two-photon biexciton excitation, optical exciton-biexciton conversion and exciton-photon interaction the peculiarities of two supershort laser pulses transmission by thin semiconductor film are investigated. Both the superluminal and ultraslow propagation of pulses and the appearance of the reflected pulses in the absence of the incident one are predicted.   Peculiarities of nonlinear nonstationary transmission (reflection) of two supershort laser pulses by a thin semiconductor film, depending on the intensities, envelope shapes, widths and time delays of the incident pulses were investigated taking into account the processes of exciton–photon interaction, optical exciton–biexciton conversion and two–photon biexciton excitation from the ground state of the crystal. We obtained the system of nonlinear differential equations, describing the time evolution of the amplitudes of excitons, biexcitons and the fields of transmitted (reflected) pulses. This system of equation consists of two nonlinear differential equations for the amplitudes of excitons and biexcitons and two or three algebraic equations for the transmitted fields depending on the initial values of incident fields. We obtained the expressions for the generalized decays of excitons and biexcitons, which depend on the time, and showed that they depend on the densities of particles and on the values of fields. We developed the theory for the case when one of the pulses excites the excitons from the ground state of the crystal, whereas the second pulse mixes the exciton and biexciton levels and results in the optical exciton–biexciton conversion and takes into account with the first pulse in the two-photon biexciton excitation. We predicted the possibility of efficient control of the transmission of one of the incident pulses by change the parameters of the second pulse and the effect of the strong time delay in transmitted pulse relative to the incident one on the frequency of exciton–biexciton transition. We demonstrated the possibility of the superluminal propagation of pulses through the film and the lethargic ultraslow propagation also depending on the initial conditions and on the order of pulse incidence. We investigated the stability of the nonstationary evolution of the pulse intensities and the densities of excitons and biexcitons. In the case of incidence of laser pulses with constant envelopes we have obtained two equilibrium points of steady state, which corresponds to the transmittance or no transmittance of the film for both pulses. We have obtained the bifurcation diagram, which describes the dependence between amplitudes of incident pulses and the parameter of the medium polarization and consists of three regions. One of these regions corresponds to the absence of transmittance of both pulses, the second region is the area of total film transmittance and the third region corresponds to the stability of both stationary points.