The invention relates to an apparatus for performing membrane gas/liquid absorption at elevated pressure, comprising a pressure vessel in which a membrane unit is provided for separate feed-through of the gas phase and the liquid phase, in such a way that exchange of components to be absorbed can take place between the gas phase and the liquid phase, the flow direction of the gas phase through the absorber being essentially perpendicular to the flow direction of the liquid phase through the absorber. The invention further relates to a method for performing gas/liquid membrane absorption employing this absorber, in particular for the absorption of CO.sub.2, H.sub.2 S, mercury (vapor) and/or water (vapor) from a gas phase at elevated pressure. The invention finally relates to a method for refining natural gas using the absorber and method according to the invention.