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Graphene oxide filled silicone rubber nanocomposites were found to possess a large nonlinear coefficient of electrical conductivity, smaller low field conductivity than that of the neat polymer and an increase in the dielectric constant over that of the polymer matrix with a very small increase in the dielectric loss. These electrical and dielectric properties make graphene oxide/silicone nanocomposites an excellent candidate for a field grading material. Possible mechanisms that lead to the observed dielectric behavior are discussed in this work. The effect of sample size and processing on the material properties is also discussed.