The spin–lattice relaxation times of 13C and 1H in hydrogenated NbCyHx (0.71 < equal y < equal 0.99, 0 < equal x < equal 0.28) 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 109 s–1 at 300 K and an activation energy of 0.18 eV; in the compounds with y > equal 0.76, this mobile fraction is absent.