The invention relates to a device for damping the oscillations of a supporting structure. Said device comprises: at least one pair of mass elements (24, 26), which are located on opposite sides of an axis (18), about which a torsional motion of the supporting structure occurs during an oscillation, each mass element being pivotally mounted in such a way that the mass of each element is distributed eccentrically around a bearing point (32, 34); at least one drive (20, 22), which adjusts the mass element by a predetermined angle on a plane running perpendicular to the axis; and a control unit, which controls at least one drive for modifying the angular position of the mass element, based on measured values of the position and/or motion of the supporting structure.