For the cubic Laves-phase compound ZrFe₂ the method of magnetic relaxation was applied in a study of low-temperature diffusion processes of hydrogen. Two relaxation maxima were observed at 82 K and 108 K with mean activation enthalpies of Q=0.14 eV and 0.23 eV and pre-exponential factors of tau ₀=10^-7 s and 4*10^-10 s, respectively. The relaxation at 82 K is assigned to H jumps during hydride formation which happens in this temperature region. The relaxation at 108 K is related to an orientation after-effect in the absence of any interaction between hydrogen atoms. This relaxation is assigned to atomic jump process of hydrogen between the preferentially occupied interstitial tetrahedral sites formed by two Fe and two Zr atoms. The activation parameters of the long-range diffusion (Q_diff=0.38 eV, D₀=3*10^-8 m² s^-1) were determined by thermal degassing.