In this paper, the nonlinear conduction behavior of high-density polyethylene (HDPE)/graphite nanosheets composites above the percolation threshold was investigated. For some samples, the I-V curves are smooth and the nonlinear term is cubic, rather than quadratic. However, for other samples, the onset of nonlinearity is accompanied by the appearance of steps in I-V curves. Furthermore, the crossover current I-c for two types of curves at which nonlinearity occurs scales with the linear conductance Sigma(1) as I-c similar to Sigma(x)(1) with x approximate to 1.28. And the second-order conductance, Sigma(2), also scales with Sigma(1) as Sigma(2) similar to Sigma(y)(1), with y approximate to 1.00. Two classical models, NLRRN (nonlinear random resistor network) and DRRN (dynamic random resistor network), cannot fully explain our experimental results. It is likely that a combination of these two models may account for the nonlinear feature better. (c) 2006 Springer Science + Business Media, Inc.