The electrochemical impedance spectra (EIS) of nonlinear and unstable electrochemical systems are numerically simulated. The effects of linear and exponential potential drifts on the EIS of anodic dissolution are examined. For direct dissolution, the numerical results are compared with the analytical solutions. For the case of dissolution via an adsorbed intermediate, Langmuir and Frumkin adsorption isotherms are considered. The simulated spectra are subjected to Kramers Kronig Transform (KKT). KKT is found to be effective in revealing the inconsistencies in the impedance spectra of unstable systems, even though it does not always flag the nonlinearities. It is shown that if the data were to be analyzed without validation by KKT, it can lead to incorrect choice of reaction mechanism or equivalent circuits. (C) 2010 Elsevier Ltd. All rights reserved.