A fuel cell, comprising a housing, at least one first polymer proton-conducting layer (1) covered by catalyst layers on both sides, gas-permeable electrodes (2) on the catalyst layers, and second layers (3) arranged on both sides of the first layers (1), whereby said second layers take the form of electro-conductive plates that are located in closely adjacent electro-conductive contact with the electrodes (2), define gas-conducting channels in conjunction with the electrodes (2), and one layer (1, 3) touches the other layer (3, 1) by means of a substantially planar surface. The first layer (1) or the second layers (3) is/are provided with an undulation, pleating and/or a deep imprint in order to form channels (4)