Hydrogen in solid solution in metals has a considerable mobility even at very low temperatures. In the Nb-O(N)-H and Nb-Ti-H systems new thermally activated anelastic processes were observed between 1.3 and 40 K for flexural resonance frequencies of 20 and 75 kHz. These effects are attributed to the motion of hydrogen kept in solution by the trapping centres formed by interstitial oxygen (nitrogen) and substitutional titanium. The internal friction curve of the Nb-O(N)-H system is characterized by a single relaxation time, whereas the relaxation spectrum of Nb-Ti-H, despite its simpler crystallographic symmetry, displays several components. The relaxation strength of both processes increases with increasing peak temperature.