NOVELTY - An electrically conductive and capacitive elastomeric composite material, comprises: (a) 10-90 wt.% of a polymer matrix that acts as binder, in addition to serving as a matrix or support; (b) 1-90 wt.% of a compound nanostructured electrical conductor, whose function is to conduct electricity through the electron transport; and (c) 20-70 wt.% of a compatibilizer compound and ionic conductor, whose main function is to support the first two components dispersed in each other, in addition to conduct electricity through ion transport.    USE - The electrically conductive and capacitive elastomeric composite material is useful in the electronic industry as capacitor for flexible rechargeable batteries that can be used in lightweight portable devices, batteries for hybrid and electric cars, solar cells attached to all kinds of lights, houses, equipment, among other materials; as well as applications in the packaging industry, especially for packaging requiring dissipation properties have electrostatic discharge (ESD), in films such as bags or bulk packaging to contain electronic circuits or any other component capable of being damaged by these burdens, where in the latter case, the material can be used directly or indirectly; directly by mixing with the polyolefin. It can also be used in combination with appropriate additives, thermoplastic resin for bodies molded parts for automotive, aerospace, electronics, home, for example in containers of fuel valves and seals, covers gadgets and electronic equipment and be material requiring ESD; the thermoplastic elastomer compound is applicable to thin films or coatings that prevent or reduce corrosion of other metal components mainly exposed to weather conditions, moisture or extreme salinity (claimed).    ADVANTAGE - The electrically conductive and capacitive elastomeric composite material can be efficiently used in the electronics industry, and preferably in the production of thin flexible rechargeable polymer batteries.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a method of making the electrically conductive and capacitive elastomeric composite material, which involves mixing 10-90 wt.% of a polymer matrix; 1-90 wt.% of a composite electrical conductor; and 20-70 wt.% of a compatibilizer compound and ionic conductor.