A high melt strength thermoplastic elastomer composition, comprising: (i) at least one linear crystalline polyolefin, having a melting temperature (Tm) of at least 100° C. and a Polydispersity Index (PI) of more than 20, determined by means of an isothermal dynamic frequency sweep at 190° C. and calculated by means of the equation PI=100,000/Gc, wherein Gc is expressed in Pascal and represents the crossover modulus (Gc=G′=G″) and (ii) at least one thermoplastic elastomer (TPE) or a blend behaving as TPE, wherein the TPE or the blend are compatible with the polyolefin (i), and have a compression set below 50% at ambient temperature after 24 h compression (ASTM D395-03, “Compression Set under constant deflection in air”), wherein the amount of component (i) is in the range of 0.1 to 15 wt % calculated on the whole of (i) and (ii); a premix (iii) useful as a homogeneous melt strain hardening additive for the preparation of this composition; a process for the preparation of shaped polymeric articles thereof, and shaped polymeric articles so prepared.