A secondarily modified block copolymer which is obtained by reacting: a primarily modified block copolymer which comprises a base block copolymer comprising at least one polymer block consisting mainly of vinylaromatic hydrocarbon monomer units and at least one polymer block consisting mainly of conjugated diene monomer units and functional−group−containing primary modifier groups bonded to the base block copolymer; with a secondary modifier having a specific functional group reactive with the functional groups of the primary modifier groups contained in the primarily modified block copolymer. Also provided is a polymer composition which comprises the secondarily modified block copolymer in combination with a thermoplastic resin and/or a rubbery polymer.
