polymeric electrolyte complexes are prepared by reacting at least one polymer represented by one of the following formulas : ## str1 ## wherein r 1 and r 2 represent hydrogen or alkyl of 1 to 4 carbon atoms ; r 3 is -- ch 2 -- c ═ ch 2 , -- m cooc ═ ch 2 ,-- ch 2 ) m cooch 2 -- c ═ ch 2 , or -- ch 2 ) m o - c ═ ch 2 ,-- ch 2 ) m o - ch 2 - c ═ ch 2 or ## str2 ## wherein r is hydrogen or methyl , m is a number from 1 to 3 and n is 0 or 1 ; at least one of r 4 , r 5 and r 6 is -- ch 2 -- c ═ ch 2 , -- ch 2 ) m cooc ═ ch 2 , -- ch 2 ) m cooch 2 oc ═ ch 2 ,-- ch 2 ) m o -- c ═ ch 2 ,-- ch 2 ) m o -- ch 2 -- c ═ ch 2 , -- ch 2 ) m conh - c ═ ch 2 or ## str3 ## wherein r is hydrogen or methyl , m is a number from 1 to 3 and n is 0 or 1 ; the remaining r 4 , r 5 and r 6 groups represent alkyl or alkylol groups of 1 to 4 carbon atoms ; b is an integer of 10 to 20 , 000 ; a / b is in a range of 0 . 01 to 2 ; c / b is in a range of 0 to 3 ; x is halogen or hydroxyl , and m is a vinyl monomer and / or a monomer having an ethylenic double bond , with a highly electrolytic polyanion dissolved in water or a mixed solvent of water and at least one member selected from the group consisting of water - miscible acids and organic solvents .