[en] In this PhD-thesis the diffusion of hydrogen and deuterium in Nb_0.8Mo_0.2 and hafnium is studied by mechanical spectroscopy. The thesis is divided in two parts: (1) H and D in Nb_0.8Mo_0.2: The diffusion of hydrogen in body-centered cubic (bcc) metals up to room-temperature is dominated by tunneling. Tunneling processes are usually more dominant at lower temperatures. Hydrogen in pure niobium is a prototype for the tunneling dominated diffusion. At temperatures below T<120 K the diffusion of hydrogen in pure niobium cannot be measured because of precipitation of hydrogen-rich phases, in which diffusion cannot take place. It was shown by neutron spectroscopy that the precipitation of hydrogen-rich phases at low temperatures is supressed in Nb_0.8Mo_0.2 for hydrogen concentrations up to x=0.05. Experiments studying the diffusion of hydrogen and deuterium in Nb_0.8Mo_0.2 were taken with mechanical spectroscopy (vibrating-reed-technique, temperature range 4.2 K< T<373 K, frequency range 50< f<5000 Hz), showing the occurence of a relaxation peak due to reorientation jumps of single hydrogen atoms (''Snoek-relaxation'') at T=80 K for H and T=105 K for D. the distinctive isotope effect shows, that diffusion in Nb_0.8Mo_0.2 is indeed dominated by tunneling. (2) H and D in hafnium: Hafnium is in the same group as titanium and zirconium. so a very similar behaviour of all the hydrides is expected. The diffusion of hydrogen at high concentrations in titanium and zirconium is well examined by various experimental techniques. For hydrogen in hafnium there exists only very few data, all taken by NMR. The goal of this work is to extend these data to an other temperature and frequency range by the use of a different experimental technique. Depending on the concentration hafnium hydride forms one of two phases: a face-centered cubic (fcc) phase for 1.53< x<1.86 and a face-centered tetragonal (fct) phase for 1.86< x<2. The diffusion of hydrogen was studied in both phases by mechanical spectroscopy (vibrating-reed-technique, temperature range 4.2K< T<373 K, frequency range 50< f< 5000 Hz). Both phases exhibit a relaxation peak of the internal friction due to forming and dissolving oh hydrogen pairs/hydrogen clusters by jumps of single hydrogen atoms (''Zener-relaxation'') in the temperature range between 275< T< 360 K. The relaxation strength in the fct-phase is unexpected high. Making use of a model for the Zener-relaxation of a concentrated lattice gas the diffusion coefficient for hydrogen is calculated. Comparision with former NMR-measurements show a good agreement of the data for the fcc-phase and a bad one for the fct-phase. (orig.)