Two different types of metallic glasses, a metal-metal-based and a metal-metalloid-based one, in both bulk and ribbon form (i.e., produced with very different quenching rates) are compared with respect to their structural relaxation behavior during continuous heating (2 K/min) in a vibrating-reed set-up (frequencies 0.2–5 kHz). The variation of damping as a function of temperature, time, and strain amplitude is shown as a measure of the content of structural relaxation centers, whose nature is studied by means of artificially introduced irregularities into the amorphous structure (i.e., by cold rolling and by hydrogen charging). The results indicate that the hydrogen damping peak, which is only observed in the Zr-based glass, is more probably due to hydrogen reorientation jumps than due to reorientation of hydrogen-related, dislocation-like distortion fields although the latter cannot be ruled out. A pronounced deformation damping peak could not be found in contrast to earlier results in the literature, probably owing to the selected degrees of deformation.