The invention relates to a composite comprising a weight fraction of single-wall carbon nanotubes and at least one polar polymer wherein the composite has an electrical and/or thermal conductivity enhanced over that of the polymer alone. The invention also comprises a method for making this polymer composition. The present application provides composite compositions that, over a wide range of single-wall carbon nanotube loading, have electrical conductivities exceeding those known in the art by more than one order of magnitude. The electrical conductivity enhancement depends on the weight fraction (F) of the single-wall carbon nanotubes in the composite. The electrical conductivity of the composite of this invention is at least 5 Siemens per centimeter (S/cm) at (F) of 0.5 (i.e. where single-wall carbon nanotube loading weight represents half of the total composite weight), at least 1 S/cm at a F of 0.1, at least 1×10−4 S/cm at (F) of 0.004, at least 6×10−9 S/cm at (F) of 0.001 and at least 3×10−16 S/cm (F) plus the intrinsic conductivity of the polymer matrix material at of 0.0001. The thermal conductivity enhancement is in excess of 1 Watt/m-° K. The polar polymer can be polycarbonate, poly(acrylic acid), poly(acrylic acid), poly(methacrylic acid), polyoxide, polysulfide, polysulfone, polyamides, polyester, polyurethane, polyimide, poly(vinyl acetate), poly(vinyl alcohol), poly(vinyl chloride), poly(vinyl pyridine), poly(vinyl pyrrolidone), copolymers thereof and combinations thereof. The composite can further comprise a nonpolar polymer, such as, a polyolefin polymer, polyethylene, polypropylene, polybutene, polyisobutene, polyisoprene, polystyrene, copolymers thereof and combinations thereof.