New perfluorovinyl monomers such as perfluorovinylamines, perfluoroallylamines and perfluorovinyl ethers bearing a dimethylamino, pyrrolidino, morpholino or piperidino group were subjected to copolymerization. Whereas perfluorovinylamines and perfluoroallylamines copolymerized only with vinylidene fluoride, the radical copolymerization of perfluorovinyl ethers and tetrafluoroethylene afforded copolymers that could be fabricated into films and had high thermal stability and gas permeability. These copolymers bearing cyclic amino groups as side chains were reacted with fuming sulfuric acid and then hydrolysed to give perfluoropolymers bearing carboxyl groups, which showed improved wettability.