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To develop an appropriate model for representing spontaneous electroencephalography (EEG) is an important and necessary work in the field of neuroscience. The Markov process amplitude (MPA) EEG model has been proposed in our previous work for representing the features of the EEG in terms of a few parameters. However, being a linear model, the linear MPA EEG model cannot perfectly describe the spontaneous EEG that displays nonlinear phenomena. Here, the nonlinear Markov process amplitude (nonlinear MPA) EEG model that includes nonlinear components is introduced. The consistent consideration of the nonlinear features of the EEG investigated by N. Wiener (1966) and P.L. Nunez (1995) can be seen from the nonlinear MPA EEG model. The similarity in the time domain and the goodness of fitting in the frequency domain with respect to the ongoing EEG are shown. As a result, the EEG power spectrum can be decomposed into the spontaneous components and the nonlinearly coupled components by use of the nonlinear MPA EEG model, which is useful for a better understanding the mechanism of the EEG generation.