The nonlinearity of an equivalent circuit with a constant-phase element (CPE) is discussed. It is based on modem nonlinear regression analysis. From the standpoint of assessing nonlinearity the following issues are considered : (a) the relationship between the linear occurrence of a given parameter in a model and the degree of nonlinear behavior of the estimator of the parameter; (b) the relationship between the total model (impedance or admittance) and its semi-models; (c) a method of obtaining good initial parameter estimates.