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The receptive-field properties of retinal ganglion cells (RGCs) provide information about early visual processing. In the primate retina, P cells form the largest class of RGCs (Rodieck, 1988). A detailed exploration of the dynamics of the two subdivisions of the P-cell receptive field--the center and the surround--was undertaken. In the preceding paper (Benardete & Kaplan, 1996), the first-order responses of the center and the surround of P cells were described, which were obtained with a new technique, the multiple m-sequence stimulus (Benardete & Victor, 1994). In this paper, the investigation of P-cell responses measured as S-potentials in the lateral geniculate nucleus (LGN) is continued, and significant nonlinear, second-order responses from the center and the surround are described. These responses are quantified by fitting a mathematical model, the linear-nonlinear-linear (LNL) model (Korenberg, 1973; Korenberg & Hunter, 1986; Victor, 1988) to the data. In a second series of experiments, demonstration that steady illumination of the surround modifies the gain of the center to contrast signals (see also Kaplan & Shapley, 1989) is made. In P ON cells, increasing the steady illumination of the surround decreases the gain and speeds up the center's first-order response. In P OFF cells, increasing the steady illumination of the surround increases the gain of the center while speeding up the response. The results of both sets of experiments are related to the known anatomy and physiology of the P cell.