A frequency-domain method is proposed for the transient analysis of grounding systems with ionized soil. The method involves two stages. First, the grounding system is transformed into a nonlinear equivalent circuit, in which the frequency-domain circuit parameters of the grounding electrodes are extracted by the method of moment (MoM) and the nonlinear part of the equivalent circuit represents the soil ionization. Soil ionization is represented by a nonlinear load whose characteristics can be specified based on either experimental data or theoretical models, without any limitations in the order of nonlinearity. In the second stage the nonlinear equivalent circuit is treated using the arithmetic operator method (AOM). The AOM uses a linear matrix transformation of spectra to perform basic arithmetic operations in the frequency-domain. The main feature of the proposed method is its efficiency in dealing with the nonlinear behavior of soil ionization in the frequency-domain solution of grounding systems by the MoM. It also enables one to consider the actual nonlinear behavior of soil ionization specified by experimental data or appropriate theoretical models. (C) 2010 Elsevier B.V. All rights reserved.