Vibration absorber arrangement suitable for damping vibrations which occur in wind turbines, tall installations or buildings, or during the erection thereof, comprising at least one swinging mass of a mass suspension, and a damping device which is connected on the one hand to the swinging mass and on the other hand to the structure to be damped of the installation or building, the damping device substantially comprising (i) a supporting construction, (ii) a transport device, which - is accommodated on or in the supporting construction, - is connected to the swinging mass, - can be moved back and forth linearly in one direction between end stop points when excited by the mass, and - is capable of converting the linear movement into a rotational movement, (iii) an articulated connecting element which is on the one hand attached to the transport device and on the other hand is connected to the swinging mass or to the structure to be damped, and an articulated connecting element which is connected on the one hand to the supporting construction and on the other hand, if the swinging mass is connected to the connecting element, to the structure to be damped, or alternatively is connected to the swinging mass if the structure to be damped is connected to the connecting element, so that said linear back-and-forth movement of the transport device takes place between the stop points when the mass is moved relative to the structure to be damped, characterized in that the damping device further comprises: (iv) at least one eddy current damping arrangement (1.4) responsible for the actual damping, which is functionally connected to the transport device and substantially has (a) at least one first element (1.1) which rotates during operation, which is designed as a disk, wheel or internal gear wheel and is equipped with magnet elements (1.4.2) or conductor elements (1.4.1) of the eddy current damping arrangement, and (b) at least one fixed second element (1.2) which is arranged opposite the first element, is connected to the supporting construction and is a disk, wheel, internal gear wheel, or a ring or a part thereof, which is correspondingly designed and located opposite in relation to the rotating element (1.1), both elements (1.1) (1.2) being arranged in parallel with one another while maintaining a substantially constant air gap, and the damping of the swinging mass and the structure being brought about by the relative rotational movement of the first element (1.1), which is driven by a corresponding linear movement of the transport device, with respect to the second element (1.2), as a result of which an eddy current is induced with a magnetic field which counteracts the rotation. (i) a supporting construction, (ii) a transport device, which - is accommodated on or in the supporting construction, - is connected to the swinging mass, - can be moved back and forth linearly in one direction between end stop points when excited by the mass, and - is capable of converting the linear movement into a rotational movement, - is accommodated on or in the supporting construction, - is connected to the swinging mass, - can be moved back and forth linearly in one direction between end stop points when excited by the mass, and - is capable of converting the linear movement into a rotational movement, (iii) an articulated connecting element which is on the one hand attached to the transport device and on the other hand is connected to the swinging mass or to the structure to be damped, and an articulated connecting element which is connected on the one hand to the supporting construction and on the other hand, if the swinging mass is connected to the connecting element, to the structure to be damped, or alternatively is connected to the swinging mass if the structure to be damped is connected to the connecting element, so that said linear back-and-forth movement of the transport device takes place between the stop points when the mass is moved relative to the structure to be damped, (a) at least one first element (1.1) which rotates during operation, which is designed as a disk, wheel or internal gear wheel and is equipped with magnet elements (1.4.2) or conductor elements (1.4.1) of the eddy current damping arrangement, and (b) at least one fixed second element (1.2) which is arranged opposite the first element, is connected to the supporting construction and is a disk, wheel, internal gear wheel, or a ring or a part thereof, which is correspondingly designed and located opposite in relation to the rotating element (1.1),