Abstract: An apparatus for suppressing torsional and flexural vibrations of rotary shafts which is arranged coaxially to the shaft, has an inner pot constructed as a flange for fixing purposes, an outer rotating ring and elastic damping elements arranged between the pot and the ring including damping elements of a first type which are fixed to the pot and the rotating ring and damping elements of a second type which are only connected to the pot and are separate from the rotating ring. The pot is further characterized by the presence of a plurality of circumferentially distributed slots so that the natural vibration behavior is influenced by speed and improved cooling is effected.