The p- and n-type bipolar redox-active radical polymer with a nitronylnitroxyl group, poly(nitronylnitroxylstyrene), expands its utilization as a cathode- or anode-active material in organic polymer-based rechargeable devices with two unprecedented configurations: a poleless battery and a “rocking-chair type” battery. These batteries exhibit remarkably high power rate capability (chargeable within 20 s) and high cycle performance.