The invention concerns a membrane for selective gas separation. The membrane consists of an ethylene oxide copolymer or a polymeric material obtained by crosslinking such a copolymer. Said copolymer is characterised in that it consists of at least 30 % in number of -CH2CH2O- units derived from ethylene oxide, and at least 2 % in number of -CHR-CH2O- units derived from an oxirane bearing a crosslinkable substituent R and/or of -CHR1-CH2O- units derived from an oxirane bearing a non-crosslinkable substituent R1. The membranes are particularly useful for separating hydrophilic gases contained in a gas mixture.