Some peculiar features of impedance spectra of a variety of porous, composite Li insertion electrodes, such as the formation of arcs and semicircles in Nyquist plots related to low frequencies are discussed. A new model that takes into account the possible nonhomogeneous (layered) distribution of the electrode's active mass on the current collector was developed. Each porous layer in the composite electrode consists of spherical particles, which insert lithium reversibly. We show that the appearance of a low-frequency semicircle (Nyquist plots) with a high capacitance value, rather than an arc or sloping lines, could be understood by adopting a nonhomogeneous, layered distribution model of the electrode's active mass, and finite values of the conductivity of the solid particle and the solution in the electrode's pores. Evidence was presented (supported by model calculations) that the low frequency semicircles observed in the Nyquist plots of these composite electrodes originate from a parallel combination of a low-frequency response of the intercalation capacity of the thinner parts and an active, highly resistive component of the impedance of the thicker parts of the electrode. A detailed comparison between the finite-space diffusion elements for spherical and linear (slab) particles is also presented.