The propagation of electromagnetic waves is investigated theoretically in organic layered conductors with metallic conductivity in magnetic fields strong enough that the characteristic radius of curvature of a conduction-electron orbit is much smaller than its mean-free path l. It is shown that when groups of charge carriers with quasi-two-dimensional and quasi-one-dimensional energy spectra coexist in such a material, the penetration depth of the waves into it, which is a strong function of the polarization of the waves and the orientation of the magnetic field, also has an interesting dependence on the magnitude of the magnetic field and the low-dimensionality parameters of the charge-carrier spectra. This property makes it possible to recover details of the Fermi surface from the experimental data.