The invention relates to a method for transferring mass between a flow of a first fluid, preferably a gas phase such as a combustion flue gas, and a flow of a second fluid, preferably a liquid phase, where the first fluid is contacted with the outer surface of porous (semi-permeable) membranes, e.g. polytetrafluoroethylene (PTFE, Teflon $m(3)) membranes, in the form of hollow fibres having gas-containing pores and contacting the second fluid with the inner surface of the membranes. Useful membranes are characterized in that they e.g. have a porosity ($g(e)) of at least 0.50, a mass transfer coefficient of e.g. at least 3 cm/s, and a tortuosity factor of e.g. at the most 1.4/$g(e) when the porosity $g(e) is lower than 0.80 and at the most 1.3/$g(e) when the porosity $g(e) is 0.80 or higher. The membranes may also be arranged in hollow tubular members where the mass transfer coefficient of the membranes is at least one tenth of the mass transfer coefficient of the gas phase. The invention also relates to an apparatus for the above-mentioned mass transfer having a tubular conduit with an open inlet end, where a part of the wall of the conduit comprises a plurality of hollow tubular members defining array(s) with interstices between the members allowing flow of the gas phase. The invention further relates to a process for absorption or desorption where porous membranes, e.g. the above-characterized membranes, are utilized and where an exceptionally low membrane area per cubic meter of gas handled is required.