We present a semimathematical model for the simulation of the impedance spectra of a rechargeable lithium batteries consisting of porous electrodes with spherical Li+ intercalation particles. The particles are considered to have two distinct homogeneous phases as a result of the intercalation and deintercalation of Li+ during charge and discharge. The diffusion of Li+ ions in the two phases and the charge transfer at the solid electrolyte interface (SEI) are described with a mathematical model. The SEI and the electrolyte are modeled using passive electronic elements. First, this model is derived for a single intercalation particle consisting of two different solid phases. This model is then transformed to a continuous model and applied to a single porous electrode, where the sizes of the particles are assumed to have on average two grain sizes where the radii are Gaussian distributions. Finally, this model is further developed to simulate the impedance of a rechargeable lithium-ion battery. (c) 2006 The Electrochemical Society.