Bimodal star-block copolymers are disclosed containing from 60 to 90% by weight of an aromatic vinyl monomer and from 40 to 10% by weight of a conjugated diene, said copolymers having the general formula:(S--S.sub.1 --B/S.sub.2 --B.sub.1).sub.m --X--(B.sub.1 --S.sub.2 /B--S.sub.1).sub.nwherein X is a polyfunctional radical, m and n are integers (being m.ltoreq.n) the sum of which is between 3 and 20 and equal to the functionality degree of the radical X, S and S.sub.1 are polymer blocks of an aromatic vinyl monomer, B.sub.1 is an elastomeric copolymer of conjugated dienic units, containing up to 20% of all the dienic units of the copolymer, and B/S.sub.2 and S.sub.2 /B are blocks of copolymers of aromatic vinyl monomer and conjugated diene of the random and/or tapered type.