A damping device, including: - a damper to be arranged on a first portion of an item of furniture or of a furniture fitting, the damper being configured to be actuated by a second portion of the item of furniture or of the furniture fitting so as to dampen a relative movement of the two portions upon a damping hub, wherein the damper includes two damping components (4a, 4b) configured to be moved relative to one another upon the damping hub, - a switchable coupling for deactivating a damping action of the damper, wherein the damper, upon the damping hub, dampens the relative movement of the two damping components (4a, 4b) when the coupling is closed, and wherein the damping action is deactivated upon a damping hub effected in the same direction when the coupling is open, wherein the switchable coupling includes a plurality of coupling elements, - wherein the switchable coupling locks one of the damping components in a first switching position, so that a relative movement between the two damping components (4a, 4b) and therewith a damping action of the damping device is produced, and that the switchable coupling releases the damping component in a second switching position, so that no relative movement of the two damping components (4a, 4b) and therewith no damping action of the damping device is produced, - a holding portion for establishing a clamping connection between one of the damping components (4a, 4a) and the coupling elements in the first switching position of the coupling, wherein the damping device includes a switching organ configured to be manually actuated, and the coupling can be switched between the first switching position and the second switching position by the switching organ. - a damper to be arranged on a first portion of an item of furniture or of a furniture fitting, the damper being configured to be actuated by a second portion of the item of furniture or of the furniture fitting so as to dampen a relative movement of the two portions upon a damping hub, wherein the damper includes two damping components (4a, 4b) configured to be moved relative to one another upon the damping hub, - a switchable coupling for deactivating a damping action of the damper, wherein the damper, upon the damping hub, dampens the relative movement of the two damping components (4a, 4b) when the coupling is closed, and wherein the damping action is deactivated upon a damping hub effected in the same direction when the coupling is open, wherein the switchable coupling includes a plurality of coupling elements, - wherein the switchable coupling locks one of the damping components in a first switching position, so that a relative movement between the two damping components (4a, 4b) and therewith a damping action of the damping device is produced, and that the switchable coupling releases the damping component in a second switching position, so that no relative movement of the two damping components (4a, 4b) and therewith no damping action of the damping device is produced, - a holding portion for establishing a clamping connection between one of the damping components (4a, 4a) and the coupling elements in the first switching position of the coupling,