This invention is based upon the discovery that a catalyst system which is comprised of (a) palladium or a palladium compound and (b) a fluorinated alcohol is effective for polymerizing norbornene-functional monomers into polynorbornene-functional polymers. It has been further discovered that this catalyst system is more effective in polymerizing certain norbornene-functional monomers that are difficult to polymerize, such as norbornene ester monomers, than prior art catalyst systems. The activity of the catalyst systems of this invention can be further improved with respect to polymerizing some monomers by including a Lewis acid and/or a ligand, such as a phosphine or a carbene, in the system. In any case, the catalyst systems of this invention offer the advantage of being soluble in a wide variety of solvents, relatively inexpensive, and capable of polymerizing many norbornene-functional monomers that are difficult to polymerize with conventional catalyst systems. The subject invention more specifically discloses a catalyst system that is especially useful for the polymerization of norbornene-functional monomers which is comprised of (a) palladium or a palladium compound and (b) a fluorinated alcohol. The present invention also reveals a process for synthesizing a norbornene-functional polymer which comprised polymerizing a norbornene-functional monomer in a solvent in the presence of a catalyst system that is comprised of (a) palladium or a palladium compound and (b) a fluorinated alcohol.