NOVELTY - Operating a fuel cell system comprising at least one fuel cell of the type comprising a cathode and an anode, each comprising catalyst, and a proton exchange membrane, where the membrane is composed of a polymeric material comprising acid-doped polybenzimidazole (PBI), involves adjusting the operating temperature of the fuel cell to 120-250 degrees C, supplying an oxidant stream to the cathode, and supplying a humidified fuel stream to the anode, where the fuel stream comprises dimethyl ether, and the dimethyl ether is directly oxidized at the anode.    USE - For operating a fuel cell system (claimed) which is used for numerous transportation or stationary applications such as portable electronics, auxiliary power units, automotive technology, uninterruptable power supplies, or stand-alone power devices.    ADVANTAGE - The humidified fuel stream is a gaseous mixture consisting of water and dimethyl ether. This constitutes a particularly simple and cost-effective solution. The operating temperature (i.e. 120-200 degrees C), constitutes an advantageous temperature interval in which fuel cell performance and lifetime are balanced in a satisfactory way. The fuel stream contains water and dimethyl ether at a molar ratio of 3.5-7.5. This stoichiometric excess of water increases the performance of the fuel cell, most likely due to increased conductivity of the proton exchange membrane and a higher rate and degree of dimethyl ether (DME) conversion. The anode catalyst comprises a platinum/ruthenium catalyst, this type of anode catalyst is advantageous with respect to a high electrode tolerance against fuel impurities. The acid-doped PBI has a proton conductivity of at least 10-3 S cm-1 at 150 degrees C and at a relative humidity of 5% to yield an advantageous performance of the fuel cell system. The acid-doped PBI has an acid-doping level of greater than or equal to 2 thus particularly high proton conductivity of the proton exchange membrane is ensured. The unreacted dimethyl ether is recirculated within the fuel cell system. This increases the system's degree of efficiency. The waste heat of the fuel cell system is used to preheat and/or vaporize water and/or dimethyl ether for the humidified fuel stream, thus reducing operation costs and improving efficiency. The humidified fuel stream is supplied at a gauge pressure of 0-50 kPag. This reduces complexity and costs, and extends the lifetime of the fuel cell system.