For an extension of the work on the ring-opening polymerizations of cyclobutane adducts of strong donor olefins and strong acceptor olefins yielding novel alternating copolymers of those olefins, the ring-opening polymerization of the cyclobutane adduct 3 of dimethyl 1,1-dicyanoethylene-2,2-dicarboxylate (DDED) and ethyl vinyl ether (EVE) is investigated. Cyclobutane 3 reacted with methanol and acetic acid at ambient temperature to yield the corresponding ring-opened adducts. The polymerizations of 3 were carried out with anionic initiators, tertiary amines, ammonium halides, and Lewis acids, respectively, according to the polymerization methods of the cyclobutane adduct 1 of tetracyanoethylene (TCNE) and EVE. All these polymerization catalysts except for ammonium halides were effective for the polymerization of 3, yielding alternating copolymers of DEED and EVE. The chain transfer reactions of the polymerization with anionic initiators are also discussed on the basis of a model reaction.