NOVELTY - The method comprises contacting a mixed gas feed stream (4) with an absorption liquid in an absorption column (1) and/or a membrane gas absorption unit at a pressure of greater than or equal to 1 bar, where the absorption liquid is selective for absorption of gases in the mixed gas feed stream so that part of the gas in the mixed gas feed stream is absorbed by the absorption liquid resulting in a rich absorption liquid, and regenerating a part of the absorption liquid by contacting the rich absorption liquid with a desorption membrane, where the pressure at a retentate side of the desorption membrane is 10-100 bar.    USE - The method is useful for separating gases in a mixed gas feed stream comprising carbon dioxide and/or hydrogen sulfide to purify gas feed stream or recover the gas feed stream.    ADVANTAGE - The method ensures cost effective separation of gases in the mixed gas feed stream with less energy consumption.    DETAILED DESCRIPTION - The method comprises contacting a mixed gas feed stream (4) with an absorption liquid in an absorption column (1) and/or a membrane gas absorption unit at a pressure of greater than or equal to 1 bar, where the absorption liquid is selective for absorption of gases in the mixed gas feed stream so that part of the gas in the mixed gas feed stream is absorbed by the absorption liquid resulting in a rich absorption liquid, regenerating a part of the absorption liquid by contacting the rich absorption liquid with a desorption membrane, where the pressure at a retentate side of the desorption membrane is 10-100 bar higher than the pressure ( greater than or equal to 10 bar) at a permeate side of the desorption membrane so that part of the absorbed gas desorbs from the rich absorption liquid and permeates through the desorption membrane for forming a lean absorption liquid, and recycling part of the lean absorption liquid for contacting with the mixed gas feed stream. The lean absorption liquid is cooled prior to contacting the mixed gas feed stream. A flow of strip gas (6) is applied at the permeate side of the desorption membrane. The rich absorption liquid is heated prior to contacting the desorption membrane. The absorption liquid comprises an ionic liquid based on an imidazolium, pyridinium or quaternary ammonium cation. The desorption membrane is a barrier for the absorption liquid, and has a thickness of 10-500 mu m. The absorption column is a packed or tray absorption column. The absorption liquid with absorbed gas is contacted with the desorption membrane in membrane gas desorption units and is connected in series and/or in parallel. The part of the gas in the mixed gas feed stream is absorbed by the absorption liquid across a membrane at elevated pressure. An INDEPENDENT CLAIM is included for an apparatus for separating gases in a mixed gas feed stream.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a gas separation apparatus.    Absorption column (1)    Desorption membrane unit (2)    Feed gas (3)    Gas stream (4)    Permeate stream (5)    Strip gas. (6)