A damping apparatus is provided for damping vibrations of a tool-holding apparatus during machining of a workpiece. The damping apparatus comprises a damping body having two ends on which a respective damping device is arranged, which comprises a bearing pin rigidly connected to the damping body and a bearing bush that surrounds the bearing pin in the circumferential direction. An annular space filled with a damping fluid is arranged between the bearing pin and the bearing bush, which annular space is sealed in the axial direction by two elastically deformable sealing rings. The two sealing rings each comprise first and second abutment regions as well as a resilient intermediate region arranged therebetween. The first abutment region is bonded to the bearing pin and the second abutment region is bonded to the bearing bush. The intermediate region is elastically deformable relative to the bearing pin and the bearing bush.