Process for the photocatalytic polymerization of a cyclical olefin or at least two different cyclical olefins in the presence of a metal compound as the catalyst, in which a photochemical ring-opening metathesis polymerization is carried out in the presence of a catalytic amount of at least one heat-stable titanium(IV), niobium(V), tantalum(V), molybdenum(VI) or tungsten(VI) compound in which a silylmethyl group and at least one halogen are bonded to the metal. The process can also be carried out by first performing the irradiation and ending the polymerization by heating. The process is suitable, for example, for the production of thermoplastic shaping compounds, coatings and images in relief.