Block copolymers compose a polyisobutylene rubbery soft segment of M.sub.n of about 5,000 to above 500,000 and glassy hard segments of M.sub.n of about 5,000 or higher and usually about 10,000 to 35,000 or more, are made by preparing a living polymer block of the polyisobutylene and then polymerizing on said living polyisobutylene block the glassy hard segments by adding thereto an electron donor having a donor number of 15 to 50 and then adding and polymerizing the monomers for the glassy hard segments. The monomers for the glassy hard segments are styrene and its derivatives and indene and its derivatives and mixtures thereof.