Process for the preparation of syndiotactic 1,2-polybutadiene having a content of 1,2 units greater than or equal to 60% and a content of syndiotactic triads greater than or equal to 50% comprising polymerising 1,3-butadiene in the presence of a catalytic system comprising: - at least one pyridyl iron complex having the general formula: in which: - R 1 represents a hydrogen atom; or a methyl group; - R 2 represents a hydrogen atom; or is selected from linear or branched C 1 -C 10, preferably C 1 -C 3, alkyl groups; - X, identical or different to one another, represent a halogen atom such as chlorine, bromine, iodine; or are selected from linear or branched, C 1 -C 20, preferably C 1 -C 15, alkyl groups, -OCOR 3 groups or -OR 3 groups in which R 3 is selected from linear or branched C 1 -C 20, preferably C 1 -C 15, alkyl groups; - n is 2 or 3; - at least one aluminoxane having the general formula: (R 4) 2 -Al-O-[-Al(R 5)-O-] m -Al-(R 6) 2 in which R 4, R 5 and R 6, identical or different to one another, represent a hydrogen atom, or a halogen atom such as, for example, 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 atoms or germanium; and m is an integer ranging from 0 to 1000; in which the molar ratio between the aluminium present in the aluminoxane having the general formula and the iron present in the pyridyl iron complex having the general formula is ranging from 5 to 20, preferably ranging from 8 to 12. - at least one pyridyl iron complex having the general formula: in which: - R 1 represents a hydrogen atom; or a methyl group; - R 2 represents a hydrogen atom; or is selected from linear or branched C 1 -C 10, preferably C 1 -C 3, alkyl groups; - X, identical or different to one another, represent a halogen atom such as chlorine, bromine, iodine; or are selected from linear or branched, C 1 -C 20, preferably C 1 -C 15, alkyl groups, -OCOR 3 groups or -OR 3 groups in which R 3 is selected from linear or branched C 1 -C 20, preferably C 1 -C 15, alkyl groups; - n is 2 or 3; - R 1 represents a hydrogen atom; or a methyl group; - R 2 represents a hydrogen atom; or is selected from linear or branched C 1 -C 10, preferably C 1 -C 3, alkyl groups; - X, identical or different to one another, represent a halogen atom such as chlorine, bromine, iodine; or are selected from linear or branched, C 1 -C 20, preferably C 1 -C 15, alkyl groups, -OCOR 3 groups or -OR 3 groups in which R 3 is selected from linear or branched C 1 -C 20, preferably C 1 -C 15, alkyl groups; - n is 2 or 3; - at least one aluminoxane having the general formula: (R 4) 2 -Al-O-[-Al(R 5)-O-] m -Al-(R 6) 2 in which R 4, R 5 and R 6, identical or different to one another, represent a hydrogen atom, or a halogen atom such as, for example, 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 atoms or germanium; and m is an integer ranging from 0 to 1000; in which the molar ratio between the aluminium present in the aluminoxane having the general formula and the iron present in the pyridyl iron complex having the general formula is ranging from 5 to 20, preferably ranging from 8 to 12.