The spin-lattice relaxation times of C-13 and H-1 in hydrogenated NbCyHx (0.71less than or equal toyless than or equal to0.99,0less than or equal toxless than or equal to0.28) and TiC0.70Hx (x = 0 and 0.30) cubic carbides were measured in a temperature range of 11-500 K. An analysis of the low-temperature relaxation data showed that hydrogen incorporation into NbCy and TiCy does not lead to a substantial change in the density of electronic states at the Fermi level. Hydrogen mobility in NbCyHx was found to strongly depend on the carbon concentration. In the compound with y = 0,71, some of the hydrogen atoms had a characteristic jump frequency of about 10(9) s(-1) at 300 K and an activation energy of 0.18 eV; in the compounds with ygreater than or equal to0.76, this mobile fraction is absent.