unsaturated monomers can comprise from 1 to 99 by weight preferably from 10 to 90 by weight particularly preferably from 50 to 90 by weight of the monomers of formula i the amount of additional olefinically unsaturated monomers includes all values therebetween especially including 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 and 85 by weight based on the total weight of the polymer or copolymer the catalysts employed in the process according to the invention are preferably based on ruthenium to which a carbene an alkylcarbene or an arylcarbene is bonded these anions a can be fluorine atoms chlorine atoms bromine atoms iodine atoms an acetate group or a trifluoroacetate group in addition a leaving group b such as for example a tricyclohexylphosphine a heterocyclic system containing double bonds which can also function as electron donor c or a transition metal complex bridged via at least two halogen atoms may be bonded to the ruthenium atom the electron donor c can be for example a heterocyclic system containing at least one double bond the following ruthenium carbene catalysts for example are suitable for the process according to the invention where cy a cyclohexyl radical ph a phenyl radical and mesi a mesityl radical r 1 r 2 r 3 r 4 and r 5 are independently h or a substituted or unsubstituted aliphatic or aromatic hydrocarbon radical having 1 20 carbon atoms the polymers prepared in accordance with the invention can be provided with a multiplicity of.