Process for preparing a random butadiene-isoprene copolymer having a high content of cis-1,4 units comprising copolymerizing butadiene and isoprene, in the presence of at least one organic solvent, and a catalytic system prepared in situ comprising: (a1) at least one neodymium carboxylate soluble in said organic solvent, containing a variable amount of water, the H2O/Nd molar ratio being between 0.001/1 and 0.50/1; (a2) at least one aluminum alkyl compound; (a3) at least one aluminum alkyl compound containing at least one halogen atom. The random butadiene-isoprene copolymer having a high content of cis-1,4 units obtained from the abovementioned process may be advantageously used in a number of applications ranging from the modification of plastics [for example, obtainment of high impact polystyrene (HIPS)], to the production of tires, in particular the production of tire treads and/or of tire sidewalls.