NOVELTY - Side chain modification of aryl main chain polymers, which can be deprotonated with organometallic compounds, with aryl-containing N-basic groups, with addition of tertiary N-basic groups containing aromatic ketone and aldehyde to metallized polymer P-Me, and protonation with water or etherification with halogen alkanes of the Me-alcoholate intermediate compound obtained is new.    USE - The ion exchange polymer membranes are useful in membrane processes such as polymer electrolyte membrane fuel cells, direct methanol fuel cells, diffusion dialysis, electrodialysis (claimed). The hydrophilic polymers are useful for reverse osmosis, nanofiltration, gas permeation, pervaporation (sic), and perstraktion (sic) (claimed).    ADVANTAGE - The polymers give membranes of good thermal and mechanical stability and avoid some drawbacks of previously used materials, e.g. poor chemical stability of vinyl polymers, e.g. polyvinylpyridine, and the carcinogenic danger of polyethyleneimines.    DETAILED DESCRIPTION - Side chain modification of aryl main chain polymers, which can be deprotonated with organometallic compounds, with aryl-containing N-basic groups, with addition of tertiary N-basic groups containing aromatic ketone and aldehyde to metallized polymer P-Me, and protonation with water or etherification with halogen alkanes of the Me-alcoholate intermediate compound obtained is new.    The aryl main chain polymers can contain groups of formula (I):    The tertiary basic N-groups can be tertiary amines or basic N-containing heterocyclic aromatic compounds, e.g. pyridine, pyrimidine, triazine, imidazole, pyrazole, triazole, thiazole, oxazole etc. These are added to the P-Me by the reaction: The polymer P can contain the residues R1 and/or R2, which are joined by bridging groups R2 to R6 and the Me-alcoholate intermediate compound is subjected to protonation with water or etherification with halogen alkanes.    INDEPENDENT CLAIMS are included for:    (1) quaternization of the tertiary-N modified polymer by reaction with halogen monoalkanes, or with a mixture of halogen mono- and dihalogen alkanes;    (2) an engineering aryl main chain polymer having an anion exchange function in the side chain, is optionally simultaneously covalently crosslinked, and can be obtained by quaternization as above; (3) preparation of covalently crosslinked anion exchange polymers and membranes by reaction in a mixture of halogen mono- and dialkanes;    (4) preparation of membranes by dissolution of a polymer in a dipolar aprotonic solvent, with subsequent deposition of the polymer solution onto a base, e.g. a glass plate, a fabric, web, or fleece as a thin film; (5) polymer membranes obtained as above;    (6) preparation of acid-base blends/acid-base blend membranes in which the basic groups in the side chain-containing polymer are mixed with a polymer containing sulfonate, phosphonate, or carboxylate groups in a dipolar aprotonic solvent, and the two polymer containing solutions are deposited on a base, e.g. a glass plate, a fabric, web, or fleece as a thin film;    (7) a process for preparation of an anion exchange polymer in which the substituted polymer, in as much as this is synthesized by reaction of tertiary N-groups of type NR2 (where R = alkyl) carrying diaromatic ketones with metallized polymer, through suspension/dissolution in dilute mineral acid with admission of air or through reaction with some other oxidizing agent in acid phase is oxidized to polymer, and contains the groups previously described.    The reaction equation (A) is: