A gripper for holding two-dimensional components with a low degree of loading, has a clamping ring connected to a controllable robot arm with a baffle plate connected to the clamping ring by a funnel-shaped component and has a gripping face which communicates with a flow system which passes through the funnel-shaped component and the baffle plate. After an excess pressure has been applied to the gripper, a negative pressure is produced on the gripping face in order to attach by suction a wafer to be gripped. A rubberized bearing surface of a bearing ring integrated in the gripping face provides a slip-resistant movement of the wafer. A sensor detects the wafer hat is attached to the gripping face by suction. In order to permit an extremely shock-resistant attachment of the wafer to be gripped on the gripping face of the gripper, a damping device which is circumferentially adapted to the gripper has a contour as viewed in plan that protrudes circumferentially above the contour of the gripper and forms a damping resistance for the wafer.