The nonlinear conduction behavior of composite materials of foliated graphite nanosheets and nylon-6 subjected to a variable direct-current electric field has been studied. Corresponding to the onset of the nonlinearity, there is a crossover current density/electric field (or current-voltage) couple. The current density or current decreases as the foliated graphite concentration decreases. Through discussions of the nonlinearities within the frameworks of the two theoretical models, the nonlinear random resistor network and the dynamic random resistor network, it is shown that neither of these models can explain fully the results obtained for this system. On the basis of the microscopic structures and conduction processes of the nanocomposites, it is found that a combination of the models can generally account for the nonlinear characteristics. (C) 2003 Wiley Periodicals, lnc. J Polym Sci Part 13: Polym Phys 42: 155-167, 2004.