TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Compounds: The compound having reactive groups is chosen from aromatic compounds of formulate (a-e).V1=reactive group, preferably halogen, hydroxy methyl, alkoxy methyl, vinyl group, allyl group, halogenated methyl, alkoxy methyl amino, bis(alkoxy methyl) amino, halogenated acyl group, isopropenyl group or allyloxy group, more preferably hydroxy methyl;W1=H, halogen, hydroxy methyl, alkoxy methyl, vinyl group, allyl group, halogenated methyl, alkoxy methyl amino, bis(alkoxy methyl) amino, halogenated acyl group, isopropenyl group, allyloxy group, hydroxyl, carboxylic acid group, sulfonic acid, amino group, amide, nitro group, aldehyde, nitrile, ester, optionally substituted (1-6C alkyl, 6-20C aryl, or 7-20C aralkyl group), more preferably hydroxyl group;andU1=direct bond or bivalent group chosen from -O-, -S-, -CO-, -COO-, -SO2-, -SO3-, phenylene group, biphenylene, anthrylene, naphthylene, 7-12C aralkylene, 1-20C alkylene, 1-20C alkylene oxy or 1-20C alkylene sulfide.The compound having reactive groups is 2,6-bis(hydroxy methyl) phenol or its derivative(s). The sulfonic acid group is introduced using sulfonating agent chosen from concentrated sulfuric acid, chlorosulfonic acid and fuming sulfuric acid, in presence of halogen solvent.    TECHNOLOGY FOCUS - POLYMERS - Preferred Conditions: The compound having reactive groups, and polyelectrolyte or polymer are reacted at 50-300degreesC, preferably 100-200degreesC, in presence of acidic catalyst.Preferred Properties: The compound (A) has molecular weight of 500 or less.Preferred Composition: The cross-linking agent is contained in an amount of 0.5-50 wt.% with respect to the polymer or electrolyte. The polyelectrolyte is chosen from polymer having ion exchange group introduced to the principal chain having aliphatic hydrocarbon; polymer having ion exchange group introduced to the principal chain having aliphatic hydrocarbon and portion of hydrogen atom substituted with fluorine; polymer having ion exchange group introduced to the principal chain having aromatic ring; polymer having ion exchange group introduced to the principal chain and having inorganic substance which does not contain carbon; and/or polymer having acidic compound introduced by ionic bond to nitrogen atom in the principal chain or side chain; and copolymer. The polyelectrolyte is preferably block copolymer containing block having sulfonic acid group and block which does not contain sulfonic acid group. At least one of the blocks contain aromatic ring in the principal chain. The ion exchange group is cation exchange group, preferably sulfonic acid group.