The invention relates to a fuel cell (1) that comprises at least one of the following components: a proton-conducting membrane (2) as the electrolyte; catalyst layers (3) that cover both sides of the membrane (2); gas-permeable electrodes in the form of an anode (4) and a cathode (5) that rest against the outward-facing surface of the catalyst layers (3); electroconductive plates (6) that come into electroconductive contact with the electrodes at close intervals and that delimit together with the electrodes channels carrying gas; and gas connections for the supply of hydrogen (H2) and oxygen (O2), respectively. The inventive fuel cell (1) is further characterized in that the membrane (2) is a crystalline or polycrystalline thin-film membrane. The thin-film membrane preferably consist of at least one layer (7) from a metal material combined with at least one electrically insulating layer (8).