Relaxation studies of the intermetallics ZrNiH x and ZrNiD x were performed using hydrogen and deuterium NMR in the  ͑x Ӎ 0.85͒ and ␥ phases ͑x Ӎ 2.6 and 3.0͒. Correlation times for atomic diffusion in the hydride were determined based on the temperature dependence of spin-lattice and spin-spin relaxation times. The hydrogen motion is shown to be thermally activated over the temperature range 300-550 K, and the activation energies for diffusion are determined. The deuterium NMR spectra exhibit incomplete line narrowing with temperature, indicating that the average electric field gradient is not zero when averaged over the deuterium atom sites of these noncubic unit cells. The temperatures of minima in T 1 and T 2 for the deuterides indicate that the motion rates are similar for the D and H systems. However, the activation energies taken from the temperature dependencies of the deuterides' T 1 and T 2 are much smaller than for the hydrides, indicating the deuteride relaxation rates have additional contributions. The spectrum of ZrNiD 1.87 reveals a coexistence of two phases, in agreement with the phase diagram.