Electrochemical impedance spectroscopy (EIS) is applied to study systems that consist of several phenomena with time constants that often differ in orders of magnitude. The final goal of using EIS is then to gain physical understanding of the investigated system and to propose a model for it. In this paper a new modelling methodology, based on a rational function, is presented. This mathematical function of the frequency is afterwards transformed into an electrical equivalent circuit (EEC) with the aid of additional physical insights. This paper describes the modelling methodology. First it is explained how the rational model is selected and estimated. Next, the transformation rules of the rational model into an EEC are illustrated. (C) 2007 Elsevier B.V. All rights reserved.