A device for the fine machining of a circumferential workpiece surface arranged eccentrically relative to an axis of a workpiece. The device comprises a pressure mechanism configured to press a fine-machining tool against the circumferential workpiece surface. The device also includes a drive unit configured to drive an active section of the pressure mechanism via a first drive and a second drive. The first drive drives the active section in a movement plane that runs crosswise to the workpiece axis along a first movement trajectory. The second drive drives the active section along a second movement trajectory that is at an angle to the first movement trajectory.