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A fault diagnosis method of nonlinear analog circuits is proposed that combines the generalized frequency response function (GFRF) and the simplified least squares support vector machine (LSSVM). In this study, the harmonic signal is used as an input to estimate the GFRFs. To improve the estimation accuracy, the GFRFs of an analog circuit are solved directly using time-domain data. The Fourier transform of the time-domain data is avoided. After obtaining the fault features, a multi-fault classifier is designed based on the LSSVM. In order to improve the training speed and reduces storage, a simplified LSSVM model is used to construct the classifier, and the conjugate gradient algorithm is used for training. The fault diagnosis simulation experiment is conducted on a biquad filter circuit to verify the proposed method. The experimental results show that the proposed method has high diagnostic accuracy and short training time.