Abstract: Conjugated diolefinic polymers having a molecular weight of less than 1,000,000 can be produced at high polymerization rates and in high yields by polymerizing a conjugated diolefin or copolymerizing a conjugated diolefin with a vinyl aromatic hydrocarbon in the presence of an alfin catalyst, in which as a molecular weight regulator is used a halogenated unsaturated hydrocarbon represented by the formula, ##EQU1## wherein R is an alkyl group having 1 to 7 carbon atoms, a vinyl group, a phenyl group, an alkyl-substituted phenyl group, a halogen atom or a hydrogen atom, and X, Y and Z which may be same or different are individually a hydrogen atom, a halogen atom or an alkyl group having 1 to 4 carbon atoms, at least one of the R, X, Y and Z being a halogen atom.