Abstract: A description follows of epoxydated block copolymers, either linear or branched, which can be defined with the following formulae:1) [A--(E--B--EPOX)].sub.n X2) A.sub.1 --(E.sub.1 --B.sub.1 --EPOX.sub.1)--A--HT--(E.sub.2 --B.sub.2 --EPOX.sub.2)3) [(E.sub.1 --B.sub.1 --EPOX.sub.1)--HT--A(E.sub.2 --B.sub.2 --EPOX.sub.2)].sub.x Xwhere A is a polyvinylaromatic block in a percentage ranging from 10 to 50% by weight, E--B--EPOX is a block composed of ethylene units, epoxydated butene and diene units in which the percentage by weight of the epoxy group ranges from 1% to 40%, HT is a tapered copolymer segment made up of hydrogenated and epoxydated diene monomeric units and vinylaromatic units whose content ranges from 0 to 20%, x is a radical having a valence ranging from 1 to 20.The block copolymers have an average molecular weight ranging from 30,000 to 400,000, a content of polyvinylaromatic blocks of between 10 and 50% by weight and a content of (E.sub.1 --B.sub.1 --EPOX.sub.1)+(E.sub.2 --B.sub.2 --EPOX.sub.