The pulsed NMR of hydrogen nuclei in LaH(,x) and YH(,x) with and without paramagnetic impurities (Ce, Nd, Gd, Dy, Er) has been studied. Measurements of proton T(,1) have been carried out in the temperature range from 77K to 800K at a resonance frequency of 400MHz;The data for both "pure" LaH(,x) (1.8 x 2.46) and YH(,x) (1.81 x 2.03) show unambiguously that the hydrogen diffusion rate increases with increasing hydrogen content. It is concluded that increased occupancy of the octahedral sublattice causes the potential wells at octahedral and tetrahedral sites to become shallower and lowers the energy barrier to motion between the two sublattices. A slope change or subsidiary minimum on the low temperature side of the principal diffusion minimum of the T(,1)(T) curve was observed in most samples, and the presence of low levels of paramagnetic impurity was found to be solely responsible for these anomalies;For systems with controlled dilute paramagnetic impurities, an additional spin-lattice relaxation process was found and appears to be essentially due to the dipolar coupling between impurity and proton moments. At low temperatures, protons far from the relaxation center are relaxed by the mechanism of spin diffusion. At higher temperatures, hydrogen diffusion becomes more rapid than spin diffusion and takes over as the mechanism for transporting distant spins to the relaxation center;This study shows that the impurity induced relaxation rate is very sensitive to the magnetic moment and relaxation rate of the impurity ion, as well as depending on the host hydride composition. Since various ions behave so differently, it is dangerous to generalize as to what effects on the proton T(,1) may be present in specific hydrides where the actual impurity content is unknown. Consequently, serious errors in deduced diffusion and electronic structure parameters may be made unless effects of impurities are recognized and allowed for.