The stability of the living ends of polymers of butadiene and isoprene has been examined at various temperatures in hexane, tetrahydrofuran and a mixture of these solvents, for the case of lithium counter ion and particularly sodium counter ion. In tetrahydrofuran, there is simultaneously a first isomerization to a carbanion, active in the polymerizations, and a destruction of the carbanions which is greatly reduced by cooling to − 40° for example. It has been possible to prepare under these conditions well-characterized block copolymers having 2, 3 and 5 blocks and for which the number average molecular weights are very close to the theoretical values. The use of two solvents successively has permitted the production of blocks with pre-determined micro-structures. If, however, the initiator is an adduct of a polycyclic hydrocarbon and sodium, transfer reactions may be observed particularly near room temperature; these reactions lead to the formation of a mixture of homopolymers when the second monomer is propylene sulphide.