NOVELTY - A sulfonated poly(arylene ether) copolymer having a crosslinkable group in a polymer chain or having a crosslinkable group in and at an end of polymer chain, is new.    USE - For forming polymer electrolyte film (claimed) useful in fuel cell, and a secondary cell.    ADVANTAGE - The polymer electrolyte film that uses the sulfonated poly(arylene ether) copolymer including the crosslinking structure, maintains the thermal stability, the mechanical stability, the chemical stability, the film formation ability and the like that are the same as or better than those of the polymer electrolyte film that is commercialized in the prior art and in addition, in terms of the proton conductivity and the cell performance, in comparison with the known polymer electrolyte film, the excessively improved effect is shown, even though it is exposed to the moisture over a long period of time, since there is no change in the electrolyte film property, the high stability is shown and it can be used in a fuel cell, and a secondary cell.    DETAILED DESCRIPTION - A sulfonated poly(arylene ether) copolymer having a crosslinkable group in a polymer chain, of formula -((CM)b-(O-SAr1-O)k-(Ar)d-(O-Ar-O)s)n- (I) or having a crosslinkable group in and at an end of polymer chain, of formula MCE-((CM)b-(O-SAr1-O)k-(Ar)d-(O-Ar-O)s)n- (II), is new.    SAr1=sulfonated aromatic (preferably 1,4-phenylene (substituted at 3 position by (SO3)- M+, naphthalene-2,7-di-yl (bi-substituted at 3 and 6 positions by (SO3)- M+, group of formula (i), naphthalene-2,3-di-yl (substituted at 7 position by (SO3)- M+, 1,4-phenylene (substituted at 3 position by (-Y1-phenyl (substituted by (SO3)- M+)), 1,4-phenylene (di-substituted at 2 and 5 positions by (-Y1-phenyl (substituted by (SO3)- M+)) or (1,4-phenylene(substituted at 2 position by (SO3)- M+))-Y1-(1,4-phenylene(substituted at 2 position by (SO3)- M+)));    Ar=none sulfonated aromatic (preferably 1,4-phenylene(tetra-substituted at 2, 3, 5 and 6 positions by F)-Y1-1,4-phenylene(tetra-substituted at 2, 3, 5 and 6 positions by F), 1,4-phenylene-Y1-1,4-phenylene, 1,4-phenylene or 1,4-phenylene(tetra-substituted at 2, 3, 5 and 6 positions by F));    Y1=single bond in which carbon and carbon are directly connected to each other, -O-, -S-, -S(O)-, -S(O)2-, -C(O)-, -C(E1)(E1)-, -Si(E1)(E1)-, -P(O)(E1)-, -A-phenyl (substituted by -A-), -A-phenylen-1-yl (substituted at 4 position by phenyl (substituted -A-)) or groups of formulae (ii) or (iii);    A1=-S(O)-, -S(O)2-, -C(O)-, -C(E1)(E1)-, -Si(E1)(E1)- or -P(O)(E1)-;    E1=H, CH3, F, CF3, 1-5C or phenylen-1-yl (penta-substituted at 2-6 positions by L1);    L1=H, F, or 1-5C;    M+=counterion such as potassium ion, sodium ion or alkyl amine having a cation charge;    CM=crosslinkable group in the polymer chain (preferably groups of formulae (iv) or (v));    J1=-Y1-phenyl (substituted by R);    R=-C?=CR1, -G1-C(R1)=C(R1)-R1 or oxirane-2-yl;    G1=single bond in which carbon and carbon are directly connected to each other, -O-, -S- or -O-C(O)-;    R1=H, F, 1-5C or phenylen-1-yl (substituted by R2);    R2=H, X, or 1-5C;    X=functional group that can perform the polymerization in conjunction with a hydroxy group of another polymer chain (disclosed);    k=0.001-1;    s=1-k;    b=0.001-1;    d=1-b;    n=a repeating unit of a polymer, and is of 10-500;and    ECM= crosslinkable group at the end of the polymer (preferably -O-phenylen-1-yl (substituted by R) or phenylen-1-yl (substituted by R)).    An INDEPENDENT CLAIM is included for a polymer electrolyte film that is crosslinked through the heat treatment and the acid treatment by using the sulfonated poly(arylene ether) copolymer (I) or (II).