NOVELTY - Chemically cross-linked polymer membrane comprises an organic polymer, an organosilsesquioxane segment, and a covalent bond between the organic polymer and the organosilsesquioxane segment.    USE - The chemically cross-linked polymer membrane is used: in a fuel cell; as a component in a filter for filtration of a liquid; to purify water; for gas separation; for separation of carbon dioxide from natural gas (all claimed). The chemically cross-linked polymer membrane is used for gas separation e.g. carbon dioxide/methane and carbon dioxide/nitrogen, oxygen/nitrogen, olefin/paraffins and for liquid separation e.g. desalination.    ADVANTAGE - The chemically cross-linked polymer membrane exhibits excellent selectivity and permeability with sustained selectivity over time by resistance to plasticization. The cross-linked organic-inorganic hybrid membranes contain covalent interpolymer-chain-connected hybrid networks: effectively reduce or stop the swelling of the polymer without disrupting the intermolecular interactions and thus reduces the mobility of the polymer main chain by enhancing the stability of polymer membrane against plasticization. The organic polymer provides: low cost; high selectivity; and easy processability.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for preparing a chemically cross-linked polymer membrane comprises: mixing an organic polymer and a cross-linking agent in an organic solvent to form a homogeneous solution; heating the homogeneous solution below 100 degrees C to react the organic polymer with the cross-linking agent to form a cross-linkable polymer solution comprising the organic polymer, the cross-linking agent, and a covalent bond between the organic polymer and the cross-linking agent; adding a catalyst to the cross-linkable polymer solution to hydrolyze and cross-link the cross-linkable polymer to form chemically cross-linked polymer comprising an organic polymer, an organosilsesquioxane segment, and a covalent bond between the organic polymer and the organosilsesquioxane segment; and fabricating a chemically cross-linked polymer membrane using the chemically cross-linked polymer comprising an organic polymer, an organosilsesquioxane segment, and a covalent bond between the organic polymer and the organosilsesquioxane segment.