The invention relates to a process for the electrochemical separation of hydrogen from a hydrogen-comprising reaction mixture R by means of a gastight membrane-electrode assembly comprising at least one selectively proton-conducting membrane and at least one electrode catalyst on each side of the membrane, where at least part of the hydrogen present in the reaction mixture R is oxidized to protons over the anode catalyst on the retentate side of the membrane and the protons are, after passing through the membrane to the permeate side, I reduced to hydrogen over the cathode catalyst and/or II reacted with oxygen over the cathode catalyst to form water, with the oxygen originating from an oxygen-comprising stream O which is brought into contact with the permeate side of the membrane, and also a reactor equipped with at least one membrane-electrode assembly.