The invention thus relates to a process for the preparation of an olefin polymer by polymerization or copolymerization of an olefin of the formula Ra --CH???CH--Rb, in which Ra and Rb are identical or different and are a hydrogen atom or a hydrocarbon radical having 1 to 14 carbon atoms, or Ra and Rb, together with the atoms joining them, can form a ring, at a temperature of -60??? to 200??? C., u