Conducting thermoplastic elastomer blends have been synthesised by deposition of polypyrrole in styrene–butadiene–styrene (SBS) block copolymers containing various amounts of ferric chloride (FeCl3). These blends have phasesegregated morphology with preferenatial deposition of polypyrrole in one of the domains as confirmed by structural investigations using optical microscopy, X‐ray diffraction and infrared spectroscopy. The electrical resistivity (ρ) for these blends shows a sharp transition in the region of 273 K and is sensitive to small mechanical deformations both in compressions and extension modes. The dependence of ρ on mechanical stress (P) follows a power law of the type ρ ∝ Pn, where n has a value between 3 and 4. These various findings have been explained on the basis of a phase‐segregated morphology having highly conducting domains separated by a semiconducting/insulating matrix, together with non‐linear conduction processes for charge transport in such heterogeneous materials. © 1994 Society of Chemical Industry