The present paper addresses the unsteady process of steam stripping of the unsaturated zone of soils contaminated with volatile nonaqueous phase liquids. First, on the basis of Darcy's law and the conservation laws of mass and energy, a one-dimensional model is derived for the propagation of the steam front in the start-up phase. It is shown that this process is governed by one dimensionless group y. Subsequently, the evaporation mechanism behind, the transport to, and the condensation at the front of volatile contaminants are considered, taking the view that nonequilibrium exists between liquid and vapor phases. The model leads to a moving boundary problem which is of special mathematical interest. By a suitable transformation of the governing partial differential equations, the problem is brought into a fixed domain and solved numerically. For a broad range of the governing dimensionless numbers, computation results are presented. The results obtained in this paper make clear the role of the prevailing principal physical phenomena during the start-up phase of the process.