Over the last few years there have been exciting achievements in designing artificial optical materials (metamaterials) with very unusual properties. For example, in some frequency regimes, they may be "left-handed" (with the left-oriented triplet of the electric, magnetic, and wave vector) and even have a negative refractive index. The experimental realization of the left-handed property is based on the resonant response of the artificial material to both electric and magnetic fields. I will discuss our recent results on propagation of extremely short electromagnetic pulses for a simple model of homogeneous doubly-resonant media, where the Duffing oscillators (anharmonic oscillators with cubic nonlinearities) represent the dielectric response of the medium, and the harmonic oscillators represent the magnetic response. The model possesses a one-parameter family of traveling-wave solutions with the structure of single or multiple humps. Rather unexpectedly, the spectrum of velocities contains a sizable discrete component. The traveling-wave solutions are found to be linearly neutrally stable. Numerical simulations demonstrate that the traveling-wave pulses behave very much like solitons: they collide in a nearly elastic fashion.