The dynamic response characterizing the induced-polarization (IP) phenomenon is modelled by a non-linear diffusion equation (Burger's equation) supplemented by relevant initial and boundary values. The analysis of the model yields a voltage step response and an impedance curve in the frequency domain which agree qualitatively with experimental measurements. Curve fits based on the model have been made in the case of electrochemical cell measurements. The diffusion coefficients estimated by means of these curves are of the same order of magnitude as those calculated using experimental measurements. The normalized transient with these diffusion coefficients agrees with observations, but probably has a shorter discharge time. We have also carried out a comparison with predictions obtained from a linear, finite diffusion layer model, thus showing that for most practical situations the nonlinear term modelling the migration effect can be neglected.