The dynamics of a nonlinear resonant tapered coupler is analyzed by using coupled-mode equations. The constituent waveguides are made of a linear host material doped with resonant impurities. Such a system allows a mechanism for all-optical switching. It is shown that nonlinear exchange between coupled waveguides originates from the group-velocity dependence on the propagating pulse power and/or area. The transmitted signal is always a multiple of the self-induced-transparency fundamental soliton. The dynamics of the pulse tuned or detuned from the resonance and with the inclusion of the material relaxation terms is discussed. In the last section the problem of soliton collision in the coupling region is considered; in this case an initial interpulse phase difference may determine a power-dependent outport switching.