A self-adjusting end position damping arrangement includes a stroke space 9 which is delimited by a movable stroke element 7, 24 and a part of the pneumatic cylinder 1, with the stroke space 9 being connected via a connecting duct 14 to the working pressure P1 which acts on the cylinder piston 22 or to the ventilation pressure (P3) in the outlet duct 3 and the stroke element 7, 24 being acted on via a damping duct 16 by the damping pressure P2 in the damping volume 19, a non-return valve 12 is arranged in the connecting duct 14 upstream of the stroke space 9, which non-return valve 12 blocks in the direction of the working pressure P1 or the ventilation pressure (P3), respectively, and a ventilation duct 5 is provided, which ventilation duct 5 can be opened by means of the movable stroke element 7, 24 and which is connected to an outlet duct 3.