In this work, the dual-phase-lagging model of the microscale heat conduction is re-derived analytically from the Boltzmann transport equation. Based on this model, the delay/advanced partial differential equations governing the microscale heat conduction are established. The method of separation of variables is applied to solve such delay/advanced partial differential equations. Finally, the oscillation of the microscale heat conduction is investigated. (c) 2005 Elsevier Ltd. All rights reserved.