Here we examine further the basis for directional selectivity (DS) in simple cells of the cat's striate cortex. We use a distinctly different input stimulus and different analysis of the output signal for the same type of space-time inseparable receptive field (RF) that was measured with flashing bars in the companion paper (Emerson, 1997). As in the companion paper, we have mimicked a popular “linear” model with a single “branch” that consists of a linear spatiotemporal filter followed by a soft threshold, which should mimic any simple cells that have a single subunit. Counterphase sinusoidal measurements of such a configuration always generate elliptically shaped polar plots of amplitude versus temporal phase, often pinched along the minor axis because of a high threshold. However, for many spatiotemporal frequencies, such polar phase plots, as measured in simple cells by others, show a consistent rotational phase skew. Here we apply counterphase analysis to the same 2-branch model as developed in the companion paper. We show that the model accounts for the skew as the summation of signals from linear filters separated spatially and temporally by approximately 90 deg (i.e. in spatiotemporal phase quadrature), each separated from the output stage by a soft-threshold nonlinearity. We also prove conclusively that such skew cannot be generated by a single-subunit configuration. This demonstration supports the proposed two-subunit structure for DS simple cells, such as in the example from the companion paper, which has strong linear contributions from its inseparable RF. The presence of at least two nonlinear subunits appears to be an obligatory concomitant of DS in all visual cortical cells. The primary function of these subunits may be to enhance the strength of responses to images moving in the preferred direction, as in complex cells. However, subunits may also aid in identifying the moving object through overcoming, at least partially, the phase-concealing properties of the neuron's threshold by generating a steady signal that effectively decreases the threshold for the preferred direction.