In a combined deceleration and acceleration device for the controlled closing and opening of, for example, furniture parts, a base part consisting of a cylinder and a guide structure is provided wherein a drag element is movably supported by the guide structure, and a piston with a piston rod is connected to the drag element which has a park position remote from the cylinder and is biased by an energy storage structure toward the cylinder for moving the piston into the cylinder in a controlled decelerating manner while carrying along the drag element and a movable part engaged with the drag element.