The invention relates to a thermoplastic elastomer composition comprising a branched olefin copolymer derived from olefinically unsaturated monomers capable of insertion polymerization having A) a T.sub.g as measured by DSC less than or equal to 10.degree. C.; B) T.sub.m greater than 80.degree. C.; C) an elongation at break of greater than or equal to 300%; D) a tensile strength of greater than or equal to 1,500 psi (10,300 kPa); and E) an elastic recovery of greater than or equal to 50%. The invention also relates to process for preparing the invention composition comprising: A) polymerizing ethylene or propylene and optionally, one or more copolymerizable monomers in a polymerization reaction under conditions sufficient to form copolymer having greater than 40% chain end-group unsaturation; B) copolymerizing the product of A) with ethylene and one or more comonomers so as to prepare said branched olefin copolymer. The branched olefin copolymer compositions of the invention are suitable as replacements for styrene block copolymer compositions and in other traditional thermoplastic elastomer applications.