A process for preparing a polymer having perfluorocyclobutane rings by the steps of (a) contacting monomers having at least two dimerizable perfluorovinyl groups; and (b) exposing the monomers to sufficient heat and for a sufficient time that a polymer containing perfluorocyclobutane rings is formed. The invention includes polymers having a backbone comprising hydrocarbyl groups, perfluorocyclobutane rings and non-carbon atoms and polymers of at least 10,000 molecular weight having repeating units [O-(CFR.sub.f).sub.n -O-perfluorocyclobutane].