Abstract: Process for the preparation of 1,2 syndiotactic polybutadiene comprising polymerizing 1,3-butadiene in the presence of a catalytic system comprising: at least one cobalt complex with a phosphine ligand having general formula (I): wherein: R1, R2 and R3, mutually identical or different, are selected from branched C4-C20 alkyl groups, preferably C4-C15, C6-C30 cycloalkyl groups, preferably Ce-Cis, said cycloalkyl groups being substituted, C6-C30 aryl groups, preferably Ce-Cis, optionally substituted; provided that at least two of R1, R2 and R3 are selected from C6-C30 aryl groups, preferably Ce-Cis, optionally substituted; X1 and X2, mutually identical or different, represent a halogen atom such as, for example, chlorine, bromine, iodine; at least one aluminoxane having general formula (II): (R4)2-AI-0-[-AI(R5)-0-]m-AI-(R6)2 (II) wherein R4, R5 and R6, mutually identical or different, represent a hydrogen atom, or a halogen atom such as, for example, chlorine, bromine, iodine, fluorine; or are selected from lin