The electrochemical characteristics of cation-exchange membranes based on polynorbornenes with fluorinated and sulfonated dicarboximide side chain groups were reported. This study was extended to a block copolymer containing structural units with phenyl and 4-oxybenzenesulfonic acid, 2,3,5,6-tetrafluorophenyl moieties replacing the hydrogen atom of the dicarboximide group. A thorough study on the electrochemical characteristics of the membranes involving electromotive forces of concentration cells and proton conductivity is reported. The proton permselectivity of the membranes is also discussed.