The invention relates to the field of membrane gas separation. A method of removing components of gas mixtures which is based on passing the components of a gas mixture through a nanoporous membrane and subsequently selectively absorbing them with a liquid absorbent that is in contact with the nanoporous membrane, wherein to prevent the gas from getting into the liquid phase of the absorbent and the liquid phase of the absorbent from getting into the gas phase, a nanoporous membrane with homogeneous porosity (size distribution less than 50%) and a pore diameter in the range of 5-500 nm is used, and the pressure differential between the gas phase and the liquid absorbent is kept below the membrane bubble point pressure. An acid gas removal performance of more than 0.3 nm3/(m2 hour) in terms of CO2 is achieved at a hollow-fiber membrane packing density of up to 3200 m2/m3, which corresponds to a specific volumetric performance of acid gas removal of up to 1000 nm3 (m3 hour). The technical result is that of providing effective extraction of undesirable components from natural and process gas mixtures.