TECHNOLOGY FOCUS - POLYMERS - Preparation: The polyarylene ether group compound is formed by polymerizing compounds of formulae (8,9) and bisphenol group compound by aromatic nucleophilic substitution.Y=same as defined above;X=univalent cation species;andZ=chlorine or fluorine.Preferred Composition: The sulfonic-acid-group content of polyarylene ether group compound is 0.3-3.5 meq/g. The polyarylene ether group compound has structural units of formulae (3,4), and contains cross-linking component in molecular chain. The cross-linking component is represented by formulae: -R1-C?=C-R2-, -R1-C?=C-R3-, -R1-CH=CH-R2- and -R1-CH=CH-R3-, preferably components of formulae (6,7).X=H or univalent cation species;R1,R2=optionally substituted 1-10C aliphatic group and aromatic group;R3=H or optionally substituted 1-10C aliphatic group and aromatic group;R4-R7=H or 1-5C alkyl;m=0-4;andn=0-1.Preferred Film: The ionic-conduction film has cross-linked structure formed by reaction of cross-linking component by heat and/or light. Preferred Cell: The fuel cell containing composite of ionic-conduction film and electrode, uses methanol as fuel. EXAMPLE - 3,3'-disulfo-4,4'-dichloro diphenyl sulfone disodium salt (in g) (17.414), 2,6-dichloro benzonitrile (4.0013), 4,4'-biphenol (10.8292), 4,4'-difluoro benzophenone (1.4101), bis(4-hydroxy-2,5-dimethylphenyl)methane, potassium carbonate (10.2711) and molecular sieve (2.61) were added to four-neck flask (100 ml). Then, nitrogen and N-methyl-2-pyrrolidone (103 ml) were added and stirred at 150degreesC for 1 hour. Then, the reaction was further carried out at 195-200degreesC for 6 hours. The resulting mixture was cooled in water, and the polymer was settled in the shape of strand. The polymer was then washed with boiling water and dried. The dried polymer (1) was dissolved in N-methyl-2-pyrrolidone (5 ml), and the resulting solution was cast on glass panel of 200 microns thickness. Then, the applied solution was dried to form a film. The glass panel with the film was immersed in water, and then processed with boiling water containing dilute sulfuric acid for removal of acid and salt components. Thus, ionic conduction film having ionic conductivity of 0.33 S/cm and ion exchange capacity of 2.21 was obtained. 3 wt.% reduction temperature of the obtained film was 373degreesC. The film had excellent dimensional stability. A composite was produced using the obtained cross-linking film. The obtained composite was used in fuel cell. The fuel cell containing the composite had favorable electric power generation characteristics.