Described is a combination of a hinge for doors or wings and a damping device in which the hinge (2) is composed of a first fastening arm (7), a second fastening arm (8) and a connecting system (9) interposed between the first and the second fastening arm (7, 8) in such manner as to make them reciprocally mobile; and in which the damping device (3) is associated with the hinge (2) at a mounting position where the damping device (3) and the hinge (2) are positioned close to each other; the damping device (3) comprises a mounting case (10), a cylinder and piston unit (11) hinged to the mounting case (10), an actuating rod (12) and a drive unit (13) interposed between the cylinder and piston unit (11) and the actuating rod (12) in order to impart to the piston (26) and cylinder (27) a relative sliding movement; the actuating rod (12) extends into the hinge (2) and is movable in a straight line between a first, extracted position, where it extends freely into the open hinge (2), and a second, retracted position, where it is in contact with a thrust surface (17) of the closed hinge (2).