The present invention therefore provides a new process for the preparation of low-viscosity fluorinated rubbers, in which at least one fluorine monomer is polymerized by free radicals in the presence of one or more compounds of the formula (I) or (II) ##STR1## wherein R.sup.1 represents a fluorine atom or a perfluoroalkyl radical having 1 to 4 carbon atoms and R.sup.2 represents a perfluoroalkyl radical having 1 to 4 carbon atoms and n=4 or 5, and, optionally, a molecular weight regulator.