We show the equivalence between the dual-phase-lagging heat conduction and the Fourier heat conduction in two-phase systems subject to lack of local thermal equilibrium. This provides an additional tool for studying the two heat-conduction processes and shows the possibility of thermal oscillation and resonance in two-phase-system heat conduction, a phenomenon observed experimentally. Such thermal waves and possibly resonance come from the macroscale coupled conductive terms. (C) 2007 Elscvicr Ltd. All rights reserved.