Carbon nanosheets (CNS) are a graphene-based material with unique properties to improve both the speed and energy storage capability of electrochemical capacitors. In this study we employ CNS to demonstrate the fastest known response time of any electrochemical capacitor, with a turn-on frequency of 36 kHz exceeding that of Al electrolytic capacitors. Further we introduce a new hybrid material, "CNS-buckypaper", i.e. CNS deposited onto freestanding buckypaper made from single-walled carbon nanotubes. Conformal deposition was achieved on similar to 3 mu m diameter nanotube bundles (or ropes) along the surface of the buckypaper which enabled a significant (similar to 4x) improvement in specific capacitance (from 60 to 230 F g(-1)) compared to as-produced buckypaper. We also discuss the synthesis, characterization, and integration of ultra-fast CNS-Ni current collectors and CNS-buckypaper electrodes into single and multi-cell supercapacitor devices. The packaged devices show high pulse-power performance at moderate energy density (similar to 1 Wh kg(-1) at 22 kW kg(-1)) indicating potential for insertion into double-layer capacitor markets. (C) 2014 Elsevier B.V. All rights reserved.