The time course of the response of a single cortical neuron to counterphase-grating stimulation may vary as a function of stimulation parameters, as shown in the preceding paper (19). The poststimulus-time histograms of the response amplitudes against time are single or double peaked, and where double peaked, the two peaks are of equal or unequal amplitudes. Furthermore, the spatial-phase dependence of cortical complex-cell responses may be a function of spatial frequency, so that the receptive field appears to have linear spatial summation at some spatial frequencies and nonlinear spatial summation at others (19). In the first part of this paper, we analyze a model receptive field that displays this behavior, and in the second part experimental data are presented and analyzed with regard to the model. The model cortical receptive field in its simplest form contains (two rows) of geniculate X-cell-like, DOG (difference-of-Gaussians)-shaped, center-surround antagonistic, circular-input subunits. We propose nonlinear summation between these two subunits, by introducing a half-wave rectification stage before pooling. The model is tested for the responses it predicts for the application of counterphase-grating stimulation. This simple model predicts the appearance of three response forms as a function of counterphase-stimulation parameters. At periodic spatial frequencies the expected-response histogram has a single peak, whose amplitude has a sinusoidal dependence on spatial phase. At spatial frequencies halfway between these, the expected-response histogram has two equal peaks whose amplitudes have a full-wave rectified sinusoidal dependence on spatial phase. At all intermediate spatial frequencies the expected-response histogram has a "mixed" form; the histogram appears sometimes with one peak, sometimes with two equal peaks, and generally with two peaks of unequal amplitude, as a function of spatial phase. Null responses are expected to appear at specific spatial phases only for the periodic spatial frequencies that give "pure" response time courses as in paragraph 5 above, and not in the more common mixed response case of paragraph 6. The analysis procedure described in the preceding paper (19) is used, separating the odd and even Fourier components of the response histograms reflecting the receptive-field intrasubunit linear summation and intersubunit nonlinear summation, respectively. We propose that this model may be used as a working hypothesis for the analysis of these aspects of the various cortical receptive-field types. Experimental data are described and discussed in terms of the model.(ABSTRACT TRUNCATED AT 400 WORDS)