Shear experiments on a molten thermoplastic elastomer (TPE) show that, above a critical stress level, the viscoelastic properties are severely affected by the flow. The TPE is a microphase-separated multiblock copolymer of poly(4-methyl-1,3-dioxolane) (PMDOL) with a copolymer of dioxolane and trioxane (PDT). The amorphous PMDOL undergoes glass transition at about −60°C, and the crystalline PDT phase melts at about 105°C. When sheared in a creep experiment at a shear stress below a critical value, the transient shear viscosity, τ y ̇ (t) , grew by two orders of magnitude without coming close to reaching steady state in the first 1000 s, and 40–80% of the total strain was recovered upon release of the shear stress. At higher shear stresses, τ y ̇ (t) passed through a maximum and then levelled off to a low plateau (steady shear viscosity), i.e. the TPE changed into a viscoelastic fluid of low viscosity. In oscillatory shear, linear viscoelasticity was limited by a critical shear stress amplitude, τ 0, which was independent of frequency and in agreement with τ c of the creep experiment. τ c dropped from 800 to 100 Pa as the temperature was increased from 120 to 160°C. Polarizing microscopy showed that the shear-induced transition is accompanied by the disruption of PDT domains which otherwise would act as physical crosslinks in the TPE melt.