Abstract: A damping cylinder having a staged rate of movement. The cylinder includes a tube, a rod extending from the tube, and a piston carried by the rod within the tube. A liquid at least partially fills the cylinder, and the piston travels within the liquid. A port through the piston permits the liquid to flow through the piston as the piston moves within the cylinder. The piston also carries a normally open flapper valve over the port. If the flow rate of the liquid through the piston is below a preselected maximum rate, the flapper valve remains open. If the flow rate of the liquid exceeds the preselected maximum rate, the flapper valve closes over the port to prohibit flow beyond the maximum rate. In preferred embodiments, a pair of flapper valves is included to limit the rate in both directions, and a bleeder bypass port is included to permit reduced rate movement of the piston after either or both of the flapper valves close.