Abstract: A description follows of random butadiene-isoprene copolymers with a trans-1,4 structure, having a butadiene/isoprene molar composition ranging from 98/2 to 32/68, the above copolymers being crystalline or amorphous depending on the isoprene content. The process for the preparation of the above copolymers is also described, in the present of a catalytic system which comprises: (a) a first component consisting of a vanadium compound selected from: (a1) compounds having general formula (Ia) VO(L)n(X)m wherein n is an integer from 1 to 3 and m ranges from zero to 2, n+m being equal to 2 or 3; (a2) compounds having general formula (Ib) V(L)p(X)q wherein p is an integer from 1 to 4, q ranges from zero to 3, the sum of p+q being equal to 3 or 4; wherein L is a bidentate ligand and X is a halogen, preferably Chlorine; (b) a second component selected from aluminoxanes and relative derivatives.