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7 pagesInternational audienceCarbon nanofibres (CNF) were dispersed into an epoxy resin using a combination of ultrasonication and mechanical mixing. The electronic transport properties of the resulting composites were investigated by means of impedance spectroscopy. It was found that a very low critical weight fraction (pc = 0.064 wt %) which may be taken to correspond to the formation of a tunneling conductive network inside the matrix. The insulator-to-conductor transition region spanned about one order of magnitude from 0.1 to 1 wt %. Far from the transition, the conductivity increased by two orders of magnitude. This increase and the low value of the conductivity were explained in terms of the presence of an epoxy film at the contact between CNF. A simple model based on the CNF-CNF contact network inside the matrix was proposed in order to evaluate the thickness of that film