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In this paper, we discuss the use of a nonlinear cascade model to predict the subthalamic nucleus spike activity from the local field potentials recorded in the motor area of the nucleus of Parkinson's disease patients undergoing deep brain stimulation. We use a segment of appropriately selected and processed data recorded from five nuclei to acquire the information of the spike timing and rhythm of a single neuron and estimate the model parameters. We then use the rest of each recording to assess the model's accuracy in predicting spike timing, rhythm, and interspike intervals. We show that the cumulative distribution function (CDF) of the predicted spikes remains inside the 95% confidence interval of the CDF of the recorded spikes. By training the model appropriately, we prove its ability to provide quite accurate predictions for multiple-neuron recordings as well, and we establish its validity as a simple yet biologically plausible model of the intranuclear spike activity recorded from Parkinson's disease patients.