A damping device for damping a motion of a movably mounted furniture part or of a movably mounted furniture fitting component of a furniture fitting includes a piston arranged in a fluid chamber. A damping effect is caused by a relative motion between the fluid chamber and the piston and the piston assumes a pressed-in end position relative to the fluid chamber at the end of the damping stroke. The damping device has a locking device which has a locking element that can be operated manually or by means of a tool in order to deactivate the damping effect. The relative position between the fluid chamber and the piston can be releasably locked in the pressed-in end position by the locking element of the locking device.