This paper investigates the modeling of non-linearity on the generation of the single trial evoked potential signal (s-EP) by means of using a mixed radial basis function neural network (M-RBFN). The more emphasis is put on the contribution of spontaneous EEG term to s-EP signal. The method is based on a nonlinear M-RBFN neural network model that is trained simultaneously with the different segments of EEG/EP data. Then, the output of the trained model (estimator) is a both fitted and reduced (optimized) nonlinear model and then provide a global representation of the passage dynamics between spontaneous brain activity and poststimulus periods. The performance of the proposed neural network method is evaluated using a realistic simulation and applied to a real EEG/EP measurement.