  Propagation of extremely short electromagnetic pulses in a homogeneous
doubly-resonant medium is considered in the framework of the total
Maxwell-Duffing-Lorentz model, where the Duffing oscillators (anharmonic
oscillators with cubic nonlinearities) represent the dielectric response of the
medium, and the Lorentz harmonic oscillators represent the magnetic response.
The wave propagation is governed by the one-dimensional Maxwell equations.
  It is shown that the model possesses a one-parameter family of traveling-wave
solutions with the structure of single or multiple humps. Solutions are
parametrized by the velocity of propagation. The spectrum of possible
velocities is shown to be continuous on a small interval at the lower end of
the spectrum; elsewhere the velocities form a discrete set. A correlation
between the number of humps and the velocity is established. The traveling-wave
solutions are found to be stable with respect to weak perturbations. Numerical
simulations demonstrate that the traveling-wave pulses collide in a nearly
elastic fashion.
