A process for preparing a solution of high molecular weight polymers of conjugated dienes in a vinylaromatic hydrocarbon by anionic polymerization of the diene in the presence of an alkyllithium as catalyst, wherein the diene is firstly polymerized in solution in an aromatic hydrocarbon which is free of ethylenic double bonds to a molecular weight Mw below about 105, a trialkylaluminum is then added in a molar excess relative to the alkyllithium, the solution obtained is diluted with the vinylaromatic compound and the polydiene is then coupled with a polyepoxide or an alkyl (meth)acrylate to give a high molecular weight polymer.