A rechargeable hybrid battery/supercapacitor electrical storage system capable of providing high energy and high power densities comprises a negative intercalation electrode (17) and a positive capacitor electrode (13) comprising an anion-adsorbing component and a cation-intercalating material combined with a separator (15) and electrically-conductive current collector elements (11, 19) to form a unitary cell structure (10). An electrolyte solution of a dissociable salt absorbed into the porous structure of the separator (15) provides complementary ion species which, supplemented by cations supplied from the positive electrode intercalation material in order to increase the energy density capability of the system, respectively reversibly intercalate into the negative electrode (17) and capacitively adsorb at the surface of the positive electrode (13) upon the application of charging current. The high density stored electrical energy may be rapidly recovered at high power over extended periods upon demand of a utilizing device and may be equally rapidly restored to stable high energy capacity through numerous charging cycles.