The basis of the complementary use of electrochemical capacitors (so-called supercapacitors) in hybrid electric power generation by rechargeable batteries and fuel cells is explored. Electrochemical capacitors are of two types: one where the interfacial double-layer capacitance of high specific area carbon materials is the basis of electric charge storage (as ions and electrons); and the other where pseudocapacitance, associated with electrosorption and surface redox processes at high-area electrode materials, e.g. RuO2, or at conducting polymers, provides the basis of charge storage. The former, double-layer, type of capacitance stores charge non-faradaically while the latter type, pseudocapacitance, stores charge indirectly through faradaic chemical processes but its electrical behaviour is like that of a capacitor. Two types of hybrid battery/capacitor system are recognized: one based on combination of an electrochemical capacitor cell with a rechargeable battery or a fuel cell in a load-leveling function, e.g. in an electric vehicle power train; and the other based on combination of a faradaic battery-type electrode coupled internally with a capacitative electrode in a two-electrode hybrid module (termed an asymmetric capacitor). Optimization of operation of such systems in terms of balancing of active masses, of power and charge densities, and choice of maximum but limited states-of-discharge, is treated.