A basic model is presented for the electric-held-driven removal of toxic ionic species from a porous medium followed by the replacement of the toxic species by nontoxic species having the same charge, The model takes into account only the principal mechanism of contaminant transport which, in the case of a charged contaminant, is electromigration. In the diffusionless approximation, the process of contaminant removal is described by a set of quasilinear hyperbolic equations which are similar to those arising in gas dynamics, chromatography, and electrophoresis. Analysis of these equations is carried out for the simple case of a ternary system consisting of two replacing cations and one anion. Depending on the relative mobilities of the toxic and nontoxic species, the medium is shown to be subdivided into either two or three moving zones with qualitatively different distributions of the species. The velocities of the zone boundaries and the time for complete removal of the contaminant from the medium are calculated analytically and interpreted physically for both constant electric current and constant potential difference across the porous medium, Theoretical predictions from the model are tested by comparing the calculated and experimentally measured conductivities of the medium, which vary with time in the course of the replacement of the toxic species by the nontoxic species of different mobilities. Conclusions regarding the process performance and efficiency are derived from the results.