NOVELTY - A monomer (A1) comprising: a poly(alkylene) oxide backbone having 20-1000 carbon atoms and 10-500 oxygen atoms, and a carbon/oxygen ratio of 1:1-10:1, is new. The monomer has 1-100 poly(alkylene) oxide side chains attached to the backbone, where each chain has 10-500 carbon atoms and 5-250 oxygen atoms, and a carbon/oxygen ratio of 1:1-10:1; and 1-8 crosslinking groups also attached to backbone. Each crosslinking group has 2-4 binding moieties that can bind with binding moieties of other monomers having the same structural features to form polymer.    USE - For producing polymers for preparing membranes for altering the compositions of a gaseous mixtures containing gases selected from H2, N2, CH4, O2, C3H8, CO2, H2S, CO, and H2O (preferably separation of individual gases from the CO2/H2 mixture) (all claimed), for separating carbon dioxide from the mixture of carbon dioxide and hydrogen obtained in the industrial production of hydrogen, for carbon dioxide/nitrogen separation, or for separating the harmful greenhouse gases from the other gases.    ADVANTAGE - The monomers provide the polymers for permeable membranes that are durable and have high permeability and selectivity for separating gases from the mixtures.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) new polymer (P1) comprising several monomers (A1) that are crosslinked to each other;    (2) preparing (M1) the monomer (A1);    (3) preparing a polymer involving reacting the branched crosslinker-containing poly(alkylene) oxide chains, prepared by the method (M1) to form a polymer via bonding between binding moieties in one chain to binding moieties in other chains;    (4) altering (M2) the composition of a gaseous mixture involving: providing a membrane formed of the polymer (P1), and passing through the membrane a gaseous mixture, containing at least a first gas and at least a second gas, where the first gas is selected from H2, N2, CH4, O2, and C3H8, and the second gas is selected from CO2, H2S, CO, and H2O;    (5) preparing (M3) a membrane involving: preparing a solution containing poly(alkylene) oxide backbones, poly(alkylene) oxide chains, and a solvent, where the backbones and the chains are dispersed in the solvent, where each of the backbones has 2-8 crosslinking groups and each of the crosslinking groups has 2-4 binding moieties; providing a layer of the solution; crosslinking the backbones via covalent bonding between binding moieties in one backbone to binding moieties in other backbones; and removing the solvent to form a membrane; and    (6) the membrane prepared by the method (M3).