By means of the vibrating reed technique, measurements of internal friction have been performed in the temperature range of 120 K < T < Tg (= glass temperature) on two amorphous alloys, each produced as ribbon and bulk material. The different contents of free volume result in an only slight shift of the onset of irreversible structural relaxation to lower temperatures (i.e., lower activation energies) for the ribbons, while considerably different amounts of structural relaxation occur. After correcting for the thermoelastic effect, the reversible structural relaxation, i.e., an approximately exponential increase of damping with rising temperature, is well described by KWW kinetics (β ≈ 0.3). For the Zr-based alloy only, a clear relaxation peak occurs in the range from 270 K to 320 K (for the first flexural vibration mode between 100 Hz and 400 Hz) induced by hydrogenation. In addition, the effect of plastic deformation on the damping behavior by cold rolling of the bulk materials has been examined.