The invention relates to a gas transfer device comprising at least two chambers and at least one gas-permeable and liquid-impermeable membrane, wherein the chambers are separated from one another by the membrane(s), and wherein the membrane(s) is/are structured on at least one side and channels and/or branching structures, in particular branched pathways, are formed on the membrane by this structure, the walls of which have a spacing of ≦500 μm, preferably of ≦350 μm, and more preferably of ≦150 μm, and the proportion of the membrane surface area which comprises channels and/or branching structures having this spacing constitutes at least 50% of the total surface area of the membrane.