We examine the modeling equations for a particular electrophoretic separation technique known as isotachophoresis. These equations form a system of advection-diffusion type and describe the time evolution of a number of charged chemical species. The transport mechanism arises from an electric field E where \(E_ x\) is a superposition of the species concentrations; thus the equations are nonlinear. The spatial domain is the real line and the concentrations satisfy Dirichlet boundary conditions at \(\pm \infty\). We show that these equations have global strong solutions that are unique in an appropriate sense.