This work shows the enhanced capability of differential impedance analysis (DIA) for recognition of CPE behavior. It is based on the procedure of a secondary DIA, which analyses the frequency dependence of the local operating model parameters' estimates in the zones where there is no adequacy between the object and the local estimator. The new algorithm is successfully examined on synthetic models of CPE, Warburg, Randles, Randles with CPE modification, simple Faradaic reaction with CPE capacitance, as well as on real data obtained on yttrium iron garnet single crystals and yttria stabilized zirconia single crystals. (C) 2004 Elsevier B.V. All rights reserved.