The invention relates to a process for the polymerization or copolymerization of at least one monomer which can be polymerized or copolymerized by the radical route in the presence of a stable free radical and of an iniferter. The presence of the stable free radical greatly modifies the behavior of the iniferter during the polymerization or copolymerization, so that undesirable reactions are much reduced. It is possible, rapidly and with a high yield, to polymerize or copolymerize in the presence of an iniferter in order to result in a polymer or copolymer with a reduced polydispersity and with a monomodal molecular mass distribution.