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A method for predicting the distortion in weakly nonlinear analog circuits is presented, which relies on the classical theory of regular perturbation. Accordingly, a nonlinear circuit is described and analyzed as a perturbation of its linearized model, and the response to a periodic signal is analytically calculated through frequency-domain recurrent formulas. The method is simple and quite straightforward to apply, as it involves the calculation of frequency-domain transfer functions and of Fourier coefficients only, making it easily adaptable to any circuit topology. The method can be a valid alternative to the Volterra series method. A relationship between the proposed method and the Volterra series method is established, showing that they lead to very similar approximants to the solution. The method has been numerically tested in practical circuits wherein the devices are modeled by polynomial and exponential nonlinearities.