If desired, the cycloolefin polymers may contain from 0 to 99% by weight, based on the total weight of the cycloolefin polymers, of polymerized units of an acyclic olefin of the formula VIII: ##STR3## where R9, R10, R11 and R12 are identical or different and are a hydrogen atom or C1 -C10 -hydrocarbon radical, e.g. a C1 -C8 -alkyl radical or C6 -C14 -aryl radical.