The invention relates to isoprene and butadiene and/or pentadiene stereoblock copolymers in which the different stereoregular blocks, joined to each other by means of a single junction point, have different structures and thermal properties. The invention also relates to a process for the preparation of the aforesaid copolymers which comprises the formation of stereoblocks in successive steps but in the presence of a single catalytic system obtained from cobalt dichloride, a phosphine and an organic compound of aluminum.