In an acceleration and deceleration device which includes at least one energy storage device and a cylinder with at least one piston movably disposed in the cylinder and moved therein by a carrier element and a sliding door including a slidable door panel provided with an acceleration and deceleration device, a second carrier element is provided guiding either the first piston or the second piston for movement in the cylinder so as to control the movement of pistons and of the sliding door near its end positions.