A method for producing highly reactive olefin polymers wherein at least 50 mol % of the polymer chains have terminal double bonds, and a novel polymerization initiating system for accomplishing the same includes contacting isobutene or an isobutene-containing monomer mixture, wherein a Lewis acid catalyst is complexed with an oxygen and/or sulfur-containing Lewis base, in an apolar solvent, and wherein an initiator is employed to initiate polymerization of the isobutene or isobutene-containing monomer mixture.