Process for working up an exhaust gas from a system for producing hydroxylamine or hydroxylammonium salts by catalytic reduction of nitrogen monoxide with hydrogen, the exhaust gas containing nitrogen monoxide, hydrogen, dinitrogen monoxide, nitrogen and ammonia. At least some of the hydrogen present in the exhaust gas is separated off from the exhaust gas by means of a gas-tight membrane-electrode assembly which comprises at least one selectively proton-conducting membrane, a retentate side, a permeate side, and, on each side of the membrane, at least one electrode catalyst, wherein, on the retentate side of the membrane, at least some of the hydrogen is oxidized to protons at the anode catalyst and the protons, after crossing the membrane, are, on the permeate side, at the cathode catalyst according to (I) reduced to hydrogen and/or (II) reacted with oxygen to form water, the oxygen originating from an oxygen-containing stream which is contacted with the permeate side.