The electric self-heating and conduction behaviors of a high-density poly-ethylene/carbon black composite at the electric-thermal equilibrium state are studied. An equation describing the current density/electric-field strength (J-E) characteristic is derived on the basis of an equation proposed for the self-heating temperature as a function of the field strength. The conduction is related to the electronic tunneling and the resistor breakdown due to self-heating that dominate the nonlinear J -E characteristic below and above a critical field strength corresponding to the J maximum, respectively. The influences of the initial structure of the percolation network and the physical state of the matrix on the conduction are also discussed on the basis of scaling arguments of the self-heating and the nonlinear J -E characteristic with respect to the initial resistivity at various ambient temperatures from 19 to 120 degrees C. (c) 2005 Wiley Periodicals, Inc.