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By using an ionic liquid of 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide, we uniformly dispersed single-walled carbon nanotubes (SWNTs) as chemically stable dopants in a vinylidene fluoride-hexafluoropropylene copolymer matrix to form a composite film. We found that the SWNT content can be increased up to 20 weight percent without reducing the mechanical flexibility or softness of the copolymer. The SWNT composite film was coated with dimethyl-siloxane-based rubber, which exhibited a conductivity of 57 siemens per centimeter and a stretchability of 134%. Further, the elastic conductor was integrated with printed organic transistors to fabricate a rubberlike active matrix with an effective area of 20 by 20 square centimeters. The active matrix sheet can be uniaxially and biaxially stretched by 70% without mechanical or electrical damage. The elastic conductor allows for the construction of electronic integrated circuits, which can be mounted anywhere, including arbitrary curved surfaces and movable parts, such as the joints of a robot's arm.