A solid polymer electrolyte material made of a copolymer comprising a repeating unit based on a fluoromonomer A which gives a polymer having an alicyclic structure in its main chain by radical polymerization, and a repeating unit based on a fluoromonomer B of the following formula (1): CF.sub.2.dbd.CF(R.sup.f).sub.jSO.sub.2X (1) wherein j is 0 or 1, X is a fluorine atom, a chlorine atom or OM {wherein M is a hydrogen atom, an alkali metal atom or a group of NR.sup.1R.sup.2R.sup.3R.sup.4 (wherein each of R.sup.1, R.sup.2, R.sup.3 and R.sup.4 which may be the same or different, is a hydrogen atom or a monovalent organic group)}, and R.sup.f is a C.sub.1-20 polyfluoroalkylene group having a straight chain or branched structure which may contain ether oxygen atoms.