Hydrogen diffusion in ZrHx (1.58<or=x<or=1.98) in the temperature range 600 K to 970 K has been measured by means of pulsed-field-gradient nuclear magnetic resonance. The activation enthalpy for hydrogen diffusion, Ha, obtained by fitting an Arrhenius expression D=D0exp(-Ha/kBT) to the diffusivities, increases sharply as x approaches the limiting value of two in good agreement with results deduced from the proton spin-lattice relaxation rate, Gamma 1, measured on the same samples. Hydrogen atoms jump predominantly between nearest-neighbour tetrahedral sites in ZrHx. The observed concentration dependence of both the effective value of H,and the pre-exponential factor D0 suggests, however, that at high hydrogen concentrations and high temperatures another interstitial site is occupied in addition. At x to 2 a small fraction of hydrogen atoms located on an interstitial site other than the tetrahedral site appears to contribute significantly to the diffusivity. The temperature and concentration dependence of the diffusion data can quantitatively be described by such a model. The activation enthalpies for all possible jumps in this system with two different kinds of site are shown to be independent of the hydrogen concentration x. The corresponding attempt frequencies nu a approximately=1013 s-1 are compatible with the picture of a classical diffusion mechanism.