The Ti 40 Zr 40 Ni 20 hydrogen-absorbing alloy was prepared in the icosahedral and amorphous phases by controlling the rotation speed of the melt-spinning method of sample preparation, and the deuterium dynamics was investigated by 2 H NMR dynamic lineshape and spin-lattice relaxation. The results were analysed by the lineshape and relaxation models that assume deuterium thermally activated hopping within a manifold of different chemical environments. The observed 8% larger activation energy for the deuterium hopping over the interstitial sites and the 10% larger static spectrum width of the amorphous phase, as compared to the icosahedral phase, can be accounted for by the larger deuterium content of the investigated amorphous sample. From the deuterium dynamics point of view, the icosahedral phase is not special with respect to the amorphous modification of the same material.