The present invention is for crosslinked membranes and in particular for crosslinked poly(ethylene oxide)-cellulose acetate-silsesquioxane (PEO-CA-Si) organic-inorganic hybrid membranes and their use in gas separation. These crosslinked PEO-CA-Si membranes were prepared by in-situ sol-gel co-condensation of crosslinkable PEO-organotrialkoxysilane and CA-organotrialkoxysilane polymers in the presence of acetic acid catalyst during the formation of membranes. The crosslinkable PEO- and CA-organotrialkoxysilane polymers were synthesized via the reaction between the hydroxyl groups on PEO (or on CA) and the isocyanate on organotrialkoxysilane to form urethane linkages under mild conditions. The crosslinked PEO-CA-Si membranes exhibited both increased selectivity of CO2/N2 and CO2 permeability as compared to a CA membrane, suggesting that these membranes are very promising for gas separations such as CO2/N2 separation.