Damping device (30) for hinges (10) for the pivotable articulation of door leaves (12) or door flaps on the carcass of pieces of furniture, in which the hinge has respectively a supporting wall mounting part (18) which can be fixed on the supporting wall (14) and a door leaf mounting part (24) which is pivotably coupled via a linkage mechanism (20; 22) to the supporting wall mounting part and can be fixed on the inner face of the door leaf or flap, and which is preferably constructed as a cup part which is countersunk and engages in a recess in the door leaf or flap and has a laterally projecting fixing flange which bears on the inner face of the door leaf.The damping device (30) has a damper housing which is provided on the door leaf mounting part (24) and which is provided in the cavity thereof with a fluid or gaseous damping medium and a resistance element which is movable relative to the damping medium and is coupled to an actuating element (39) which extends out of the housing. At least during part of the pivoting movement of the mounting parts (18, 24) relative to one another the actuating element is in engaged connection directly or indirectly with the supporting wall mounting part (18) and transmits to the resistance element the relative movement of the mounting parts as they pivot.The damper housing (32) is a separate component which is provided with laterally projecting fixing flanges (38, 46) which can be fixed on the fixing flanges of the door leaf mounting part (24).