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: wherein: - R 1, R 2 and R 3, mutually identical or different, are selected from, branched C 4 -C 20 alkyl groups, preferably C 4 -C 15, C 6 -C 30 cycloalkyl groups, preferably C 6 -C 15, said cycloalkyl groups being substituted, C 6 -C 30 aryl groups, preferably C 6 -C 15, optionally substituted; provided that at least two of R 1, R 2 and R 3 are selected from C 6 -C 30 aryl groups, preferably C 6 -C 15, optionally substituted; - X 1 and X 2, mutually identical or different, represent a halogen atom such as chlorine, bromine, iodine; - at least one aluminoxane having general formula: (R 4) 2 -Al-O-[-Al(R 5)-O-] m -Al-(R 6) 2 wherein R 4, R 5 and R 6, mutually identical or different, represent a hydrogen atom or a halogen atom such as chlorine, bromine, iodine, fluorine; or are selected from linear or branched C 1 -C 20 alkyl groups, cycloalkyl groups, aryl groups, said groups being optionally substituted with one or more silicon or germanium atoms; and m is an integer ranging from 0 to 1000; said process being carried out at a temperature ranging from 0°C to +60° C, preferably ranging from 0°C to +30°C. - at least one cobalt complex with a phosphine ligand having general formula: wherein: - R 1, R 2 and R 3, mutually identical or different, are selected from, branched C 4 -C 20 alkyl groups, preferably C 4 -C 15, C 6 -C 30 cycloalkyl groups, preferably C 6 -C 15, said cycloalkyl groups being substituted, C 6 -C 30 aryl groups, preferably C 6 -C 15, optionally substituted; provided that at least two of R 1, R 2 and R 3 are selected from C 6 -C 30 aryl groups, preferably C 6 -C 15, optionally substituted; - X 1 and X 2, mutually identical or different, represent a halogen atom such as chlorine, bromine, iodine; - at least one aluminoxane having general formula: (R 4) 2 -Al-O-[-Al(R 5)-O-] m -Al-(R 6) 2 wherein R 4, R 5 and R 6, mutually identical or different, represent a hydrogen atom or a halogen atom such as chlorine, bromine, iodine, fluorine; or are selected from linear or branched C 1 -C 20 alkyl groups, cycloalkyl groups, aryl groups, said groups being optionally substituted with one or more silicon or germanium atoms; and m is an integer ranging from 0 to 1000; said process being carried out at a temperature ranging from 0°C to +60° C, preferably ranging from 0°C to +30°C. - R 1, R 2 and R 3, mutually identical or different, are selected from, branched C 4 -C 20 alkyl groups, preferably C 4 -C 15, C 6 -C 30 cycloalkyl groups, preferably C 6 -C 15, said cycloalkyl groups being substituted, C 6 -C 30 aryl groups, preferably C 6 -C 15, optionally substituted; provided that at least two of R 1, R 2 and R 3 are selected from C 6 -C 30 aryl groups, preferably C 6 -C 15, optionally substituted; - X 1 and X 2, mutually identical or different, represent a halogen atom such as chlorine, bromine, iodine; - at least one aluminoxane having general formula: (R 4) 2 -Al-O-[-Al(R 5)-O-] m -Al-(R 6) 2 wherein R 4, R 5 and R 6, mutually identical or different, represent a hydrogen atom or a halogen atom such as chlorine, bromine, iodine, fluorine; or are selected from linear or branched C 1 -C 20 alkyl groups, cycloalkyl groups, aryl groups, said groups being optionally substituted with one or more silicon or germanium atoms; and m is an integer ranging from 0 to 1000; said process being carried out at a temperature ranging from 0°C to +60° C, preferably ranging from 0°C to +30°C. wherein R 4, R 5 and R 6, mutually identical or different, represent a hydrogen atom or a halogen atom such as chlorine, bromine, iodine, fluorine; or are selected from linear or branched C 1 -C 20 alkyl groups, cycloalkyl groups, aryl groups, said groups being optionally substituted with one or more silicon or germanium atoms; and m is an integer ranging from 0 to 1000; said process being carried out at a temperature ranging from 0°C to +60° C, preferably ranging from 0°C to +30°C.