Hydrogen permeation through amorphous and recrystallized foils of Fe-based alloys was investigated. It was found that surface layers of both types of samples were enriched by metalloids. These layers prevented permeation of hydrogen from molecular and atomic phases. Only the ionization of the gas in glow discharge near the upstream side of foils resulted in big permeation fluxes. Kinetics of flux relaxation to the steady-state values revealed reversible trapping in amorphous alloy. Permeation flux demonstrated Arrhenius linear dependence for recrystallized samples and non-monotonous for amorphous ones. Values of steady-state flux through amorphous foils were several times higher than through ordered samples at temperatures below 200 degreesC. The mechanism of hydrogen transport is proposed taking into account re-emission and diffusion processes. Activation energies for thermal desorption and diffusion are evaluated.