The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.