NOVELTY - A non-porous polymer membrane (2), especially made from polyimide or polyether ketone, has a covering layer preferably less than 100 nm in thickness, made from a precious metal or a precious metal alloy. The membrane structure (1) and the membrane itself (2), are temperature-resistant to above 200degreesC, preferably above 300degreesC. Polymer membrane (2) thickness is 1-50 microns, especially 5-20 microns. It is fibre-reinforced and takes the form of a single- or multi-layer.    USE - A membrane for separating hydrogen or oxygen from a gas mixture (5) for vehicular, petrochemical, power or flight emergency applications The membrane structure (1) is used to separate hydrogen or oxygen from a gas mixture. This is supplied to the membrane at a temperature exceeding 200degreesC, especially exceeding 300degreesC, and/or under a pressure exceeding 0.1 MPa and preferably above 5 MPa (all claimed). Example applications include: separation of CO from reformer gas for supply to a fuel cell, hydrogen recovery in petrochemical plants, recovery of pure oxygen for power stations with internal coal gasification and continuous emergency supply of oxygen to passengers in aircraft.    ADVANTAGE - The new membrane construction offers simple, cost-effective separation at comparatively high temperatures, pressures and rates. Very high separation throughputs in terms of mass- or volumetric flowrate are achieved per unit area, for a given pressure difference, as a result of the thin layers specified.    DETAILED DESCRIPTION - The thickness of the covering layer (3) is less than 50 nm, especially 25 nm or less. It is less than 10%, especially less than 1% of the polymer membrane thickness. The covering layer is sputtered or vapor-deposited onto the polymer membrane, especially by plasma-coating. In the membrane construction (1), a preferably porous or grid-like carrier (4) supports the polymer membrane (2), especially on the side facing away from the covering layer.    DESCRIPTION OF DRAWING(S) - A schematic cross section of an implementation is presented.    membrane structure (1)    non-porous polymer membrane (2)    covering layer (3)    porous or grid-form carrier (4)    gas mixture (5)