A process for the continuous synthesis of a diene elastomer by n reactors r1 to rn, n ranging from 2 to 15, is provided. The reactor r1 is fed by an input solution comprising a solvent, one or more monomers, an anionic polymerization initiator and a polar agent, one or more of the reactor(s) r2 to rn also being fed by reinjection of a purified solution comprising solvent and/or monomer(s), the purity of the or of each reinjected solution being such that the proportion of the number of dead chains in the output stream from the reactor rn is less than 30%, of the number of living chains initiated in the reactor r1, the temperature of each reactor ranging from 20 to 150° C. and being greater than or equal to the temperature of the reactor which immediately precedes it, the diene elastomer having a polydispersity index of 1.1 to 2.