To meet the increasing demand, for stretchable conductive materials in a wide range of applications, innovative conductors based on single wall carbon nanotubes (SWCNT) self-grafted on different polymer films, are assembled. Aiming at a simple technology for flexible and stretchable electronic devices, and contrary to what commonly reported for carbon nanotubes (CNT), no chemical functionalization of SWCNT is necessary for stable grafting onto several polymeric surfaces. The novelty and functionality of our composite materials stand in the synergy among the intrinsic biocompatibility of CNT, a fully inert material, their electrical conductivity, and the stretchable-viscoelastic properties of the polymer-nanotube bundles composites. Electrical characterization of both unstretched and strongly stretched planar film conductors is provided, demonstrating the use of this new composite material for technological application. Also, an insight into the mechanisms of strong adhesion to the polymer is obtained by scanning electron microscopy (SEM) of the surface composite. As an example of technological application of such stretchable circuitry, the electrical functionality of a carbon nanotube-based six-sensor (electrode) grid is used to record subdural electrocorticograms in freely-moving laboratory rats over approximately three months.