An improved process is described for preparing conjugate diolefin polymers or copolymers having a high content of 1,4-cis units and high chain linearity, the process using a particular catalytic system prepared from a compound of a metal chosen from those of Group III B of the Periodic System which have an atomic number of between 21 and 103, preferably neodymium, an organic halogen derivative, and an aluminium alkylhydride or trialkyl.