this invention relates to a perfectly or partially crosslinked olefinic thermoplastic elastomer composition which comprises 10 to 90 parts by weight of a crystalline polyolefin , 90 to 10 parts by weight of an olefin - based copolymer rubber and being 100 parts by weight ) and 3 to 100 parts by weight of a paraffinic mineral oil softening agent having an evaporation loss of 0 . 4 % by weight or less at a condition of 200 ° c ., atmospheric pressure and 1 hour and having a kinetic viscosity of 50 to 250 cst ; an olefinic thermoplastic elastomer composition which is obtainable by subjecting a mixture including 40 to 85 parts by weight of an ethylene - based copolymer rubber , 60 to 15 parts by weight of an olefinic resin and 45 parts by weight or less of a softening agent , and being 100 parts by weight ] to dynamic heat treatment in the presence of a crossliking agent and which has a gloss value of 80 % or more and a haze value of 10 % or less on glass plate when subjected to the fogging test at a condition of 100 ° c . and 3 hours according to the prescription of a method of din 75201 ; and a manufacturing method and use of the compositions .