Process for the preparation of (co) polymers of conjugated dienes which comprises polymerizing at least one conjugated diene in the presence of a catalytic system comprising at least one oxo-nitrogenated complex of cobalt having general formula (I), wherein: —R1 and R2, equal to or different from each other, represent a hydrogen atom; or they are selected from linear or branched C1-C20, preferably C1-C15, alkyl groups, optionally halogenated; cycloalkyl groups optionally substituted; aryl groups optionally substituted; —Y represents an oxygen atom; or a group —N—R3 wherein R3 represents a hydrogen atom, or it is selected from linear or branched C1-C20 preferably C1-C15, alkyl groups, optionally halogenated, cycloalkyl groups optionally substituted-; aryl groups optionally substituted; or, when Y represents a group —N—R3, R2 and R3 can be optionally bound to each other to form, together with the other atoms to which they are bound, a cycle containing from 3 to 6 carbon atoms, saturated, unsaturated, or aromatic, optionally substituted with linear or branched C1-C20 preferably C1-C15, alkyl groups, said cycle optionally containing heteroatoms such as, for example, oxygen, sulfur, nitrogen, silicon, phosphorous, selenium; —X1 and X2, equal to or different from each other, represent a halogen atom such as, for example, chlorine, bromine, iodine; or they are selected from linear or branched C1-C20 preferably C1-C15, alkyl groups, —OCOR4 groups or —OR4 groups wherein R4 is selected from linear or branched C1-C20 preferably C1-C15, alkyl groups.