A hybrid electrode for a high power, high energy, electrical storage device contains both a high-energy electrode material (42) and a high-rate electrode material (44). The two materials are deposited on a current collector (40), and the electrode is used to make an energy storage device that exhibits both the high-rate capability of a capacitor and the high energy capability of a battery. The two materials can be co-deposited on the current collector in a variety of ways, either in superimposed layers, adjacent layers, intermixed with each other or one material coating the other to form a mixture that is then deposited on the current collector.