The present invention relates to an olefinic thermoplastic elastomer
composition which comprises a crystalline polyolefin resin (A), an
ethylene-.alpha.-olefin-non-conjugated polyene copolymer rubber (B) and at
least on rubber (C) selected from polyisobutylene, butyl rubber and a
propylene-ethylene copolymer rubber having a propylene content of 50 mol %
or more or an ethylene-.alpha.-olefin copolymer (D) having a density of
0.870 to 0.940 (g/cm.sup.3) and an ethylene content of 85 mol % or more,
said ethylene-.alpha.-olefin-non-conjugated polyene copolymer rubber (B)
being crosslinked thermoplastic elastomer composition, being obtained by
random copolymerization of ethylene, and .alpha.-olefin having 3 to 20
carbon atoms and a non-conjugated polyene in the presence of a metallocene
catalyst, (1) containing the unit (a) derived from the ethylene and the
unit (b) derived from the .alpha.-olefin in a molar ratio of 40/60 to 95/5
[(a)/(b)], (2) having an iodine value of 1 to 50 and (3) having an
intrinsic viscosity [.eta.] measured in decalin at 135.degree. C. of 1.0
to 10 dl/g; and relates to a method for manufacturing the same.