Abstract: A process for separating and/or recovering gases from gas and/or gas vapor mixtures includes a membrane separating device to which a gas and/or gas vapor mixture is supplied, the latter being separated in the membrane separating device into a permeate, which is enriched with gas, and a retentate, which is depleted of gas. A first membrane separating device and a downstream second membrane separating device are provided, to which is supplied (at its inlet end) the retentate from the first membrane separating device, the first membrane separating device having a membrane which is selective for higher hydrocarbons in the gas and/or gas vapor mixture to be separated and in that the second membrane separating device has a membrane which is selected for gases of small molecular diameter.