Process for the preparation of polybutadiene with a low branching degree which comprises:

(a) a first polymerization step of butadiene in the presence of organic solvents and in the presence of a catalytic system comprising (a1) a derivative of neodymium;

(a2) an aluminum alkyl having general formula (I) AlR₁R₂R₃;

(a3) an organo aluminum derivative containing at least one halogen atom, preferably chlorine;

the above first step being carried out up to a conversion of butadiene 98% to give a linear polybutadiene (g_m=1) with a content of 1,4-cis units greater than 93% and a Mw/Mn ranging from 2.2 to 2.9;

(b) treatment of the polymeric solution obtained at the end of step (a) with a peroxide,

(c) recovery of the polybutadiene with a low branching degree obtained at the end of step (b).