In a combined acceleration and deceleration device with a carrier housing and a carrier element which is movable along at least one guide track of the carrier housing between a force and/or form-locking park position and an end position under the control of an acceleration arrangement and a deceleration arrangement including a hydraulic cylinder-piston unit with a spring return structure. The cylinder-piston unit carries a guide member which is guided by the guide track and has a curved stop surface and the carrier element has a curved push surface with the push surface area and the stop surface area having different radii of curvature so that they contact each other maximally along a contact line.