The invention relates to a process for converting aliphatic hydrocarbons having from 1 to 4 carbon atoms into aromatic hydrocarbons, which comprises the steps: a) reaction of a feed stream E comprising at least one aliphatic hydrocarbon having from 1 to 4 carbon atoms in the presence of a catalyst under nonoxidative conditions to give a product stream P comprising aromatic hydrocarbons and hydrogen and b) electrochemical removal of at least part of the hydrogen formed in the reaction from the product stream P 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 is oxidized to protons over the anode catalyst on the retentate side of the membrane and the protons are, after passing through the membrane on the permeate side, reacted with oxygen to form water over the cathode catalyst, with the oxygen originating from an oxygen-comprising stream O which is brought into contact with the permeate side of the membrane.