The novel thermoplastic elastomer composition of the present invention,
which comprises an isobutylene block copolymer (A) containing a polymer
block composed predominantly of isobutylene and a polymer block composed
predominantly of an aromatic vinyl compound and an alkenyl-terminated
isobutylene polymer (B), is highly flexible, and satisfactory in good
moldability, rubber-like characteristics, mechanical strengths, permanent
compression set characteristics and vibration damping properties.