1. We have analyzed receptive fields (RFs) of directionally selective (DS) complex cells in the striate cortex of the cat. We determined the extent to which the DS of a complex cell depends on spatially identifiable subunits within the RF by studying responses to an optimally oriented, three-luminance-valued, gratinglike stimulus that was spatiotemporally randomized. 2. We identified subunits by testing for nonlinear spatial RF interactions. To do this, we calculated Wiener-like kernels in a spatial superposition test that depended on two RF positions at a time. The spatial and temporal separation of light and dark bars at these two positions varied over a spatial range of 8 degrees and a temporal range of +/- 112 ms in increments of 0.5 degree and 16 ms, respectively. 3. DS responses in complex cells cannot be explained by their responses to single light or dark bars because any linear superposition of responses whose time course is uniform across space shows no directional preference. 4. Nonlinear interactions between a flashed reference bar that is fixed in position and a second bar that is flashed at surrounding positions help explain DS by showing multiplicative-type facilitation for bar pairs that mimic motion in the preferred direction and suppression for bar pairs that mimic motion in the null direction. Interactions in the preferred direction have an optimal space/time ratio (velocity), exhibited by elongated, obliquely oriented positive domains in a space-time coordinate frame. This relationship is inseparable in space-time. The slope of the long axis specifies the preferred speed, and its negative agrees with the most strongly suppressed speed in the opposite direction. 5. When the reference bar position is moved across the RF, the spatiotemporal interaction moves with it. This suggests the existence of a family of nearly uniform subunits distributed across the RF. We call the subunit interaction, as averaged across the RF, the "motion kernel" because its spatial and temporal variables are those necessary to specify the velocity, the only parameter that distinguishes a moving image from a temporally modulated stationary image. The nonlinear interaction shows a spatial periodicity, which suggests a mechanism of velocity selectivity for moving extended images.(ABSTRACT TRUNCATED AT 400 WORDS)