The present invention relates to a process for controlled radical polymerization using an organosulfur reversible chain transfer agent which consists in preparing polymers having a molar weight of greater than 100 000 g/mol, with a polydispersity index of less than 1.2 for molar weights of less than 200 000 g/mol and of less than 1.4 for molar weights of greater than 200 000 g/mol, with a degree of conversion of monomer of greater than 75% and a polymerization time of less than 8 h, characterized by the control of the flux of initiator radicals in the polymerization medium.The control of the flux of initiator radicals can be achieved by the use of two appropriate polymerization temperatures T.sub.1 and T.sub.2 or by use of an initiator having a decomposition rate constant which is greater than that of azobisisobutyronitrile at the same temperature.