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 and a process for preparing impact-modified polymers of vinylaromatic compounds is described. The first process comprises firstly polymerizing the diene in solution in an aromatic hydrocarbon which is free of ethylenic double bonds to a molecular weight below about 105, then adding a trialkylaluminum in a molar excess relative to the alkyllithium, diluting the solution obtained with the vinylaromatic compound and then coupling the polydiene with a polyepoxide or an alkyl (meth)acrylate to give a high molecular weight polymer. The solution obtained in this way is further processed to give an impact-modified polymer of a vinylaromatic hydrocarbon by polymerizing the solution prepared as described, if desired after addition of further amounts of a vinylaromatic compound, in a manner known per se.