The pi-allylnickel-catalyzed coordination cyclopolymerization of a bis(allene) possessing a malonate moiety, diethyl bis(2,3-butadienyl)malonate, gave a polymer which is soluble in organic solvents. The polymer was composed of an almost comparable content of the 1,2- and the 2,3-polymerized units. The polymerization was supposed to proceed through the selective formation of a six-membered ring unit in the main chain by means of the cyclopolymerization of the bis(allene). That is, the intramolecular attack of the growing allylnickel species generated from the first allene moiety upon another one was supposed to give the 1,2-polymerized unit having the six-membered ring system while the intermolecular attack of the allylnickel species derived from the second allene provides the 2,3-polymized unit selectively as is the case of the monofunctional allenes. The effect of the polymerization conditions such as the concentration of the monomer on the polymerization behavior is also described.