The variation of the hydrogen permeability with time was monitored during the permeation of hydrogen through metallic amorphous membranes of Ni45−XNb30Zr25CoX (X=0, 7.5, and 15 at%) in the temperature range of 350 to 450 °C. For tests performed between 3 and 5 bars, the alloy with the medium content of Co, i.e., 7.5 at%, had the most pronounced degradation while the alloy without Co showed less of a decrease in the hydrogen permeability with time. The change in the hydrogen permeability with the Co content was discussed in connection with the difference in the activation barrier energy for crystallization in the alloys.