The hydrogen permeability of amorphous and recrystallized Fe alloys is investigated. It is found that the surface layers of both samples are enriched with metalloids, which interfere with the penetration of hydrogen from the molecular and atomic phases. The kinetics of curves of flow transition to a steady state upon ion irradiation in an amorphous alloy points to processes of reversible capture. The penetrating flow demonstrates Arrhenius dependence on temperature in the case of recrystallized samples and nonmonotonic dependence on temperature in the case of amorphous samples. A model of hydrogen penetration is suggested, which includes the reemission and diffusion processes; and estimates are obtained of the energy of activation of thermodesorption and diffusion.