Energy storage device having the features a: the energy storage device comprises a composite of a positive electrode in the for of a layer, a negative electrode in the form of a layer and a separator in the form of a layer which is arranged between the positive electrode in the form of a layer and the negative electrode in the form of a layer, b: the electrodes (102, 103) each comprise an electrochemical active component, c: the separator in the form of a layer comprises a porous sheet structure, d: the energy storage device comprises an electrolyte which ensures an ion current between the electrodes (102, 103) during charging and/or discharging of the energy storage device, and e: the energy storage device comprises a housing made up of a first housing part and a second housing part, f. the negative electrode is a metal-based anode which comprises a metal which is oxidized during charging of the energy storage device as electrochemical active component, and g. the positive electrode is an air cathode and comprises a catalyst, which makes reduction of atmospheric oxygen with uptake of electrons into the air cathode possible, as electrochemical active component, and also the additional characterizing features h: the porous sheet structure comprises a central region in which its pores are filled with the electrolyte and also a strip-like peripheral region enclosing the central region, in which peripheral region the pores of the porous sheet structure are not filled with the electrolyte, and i: the first housing part and the second housing part are joined to one another by means of a circumferential sealing frame which is formed by a sealant which has been applied to the porous sheet structure in the peripheral region. a: the energy storage device comprises a composite of a positive electrode in the for of a layer, a negative electrode in the form of a layer and a separator in the form of a layer which is arranged between the positive electrode in the form of a layer and the negative electrode in the form of a layer, b: the electrodes (102, 103) each comprise an electrochemical active component, c: the separator in the form of a layer comprises a porous sheet structure, d: the energy storage device comprises an electrolyte which ensures an ion current between the electrodes (102, 103) during charging and/or discharging of the energy storage device, and e: the energy storage device comprises a housing made up of a first housing part and a second housing part, f. the negative electrode is a metal-based anode which comprises a metal which is oxidized during charging of the energy storage device as electrochemical active component, and g. the positive electrode is an air cathode and comprises a catalyst, which makes reduction of atmospheric oxygen with uptake of electrons into the air cathode possible, as electrochemical active component, and also the additional characterizing features h: the porous sheet structure comprises a central region in which its pores are filled with the electrolyte and also a strip-like peripheral region enclosing the central region, in which peripheral region the pores of the porous sheet structure are not filled with the electrolyte, and i: the first housing part and the second housing part are joined to one another by means of a circumferential sealing frame which is formed by a sealant which has been applied to the porous sheet structure in the peripheral region.