Spatial and temporal properties related to direction selectivity of both simple and complex type visual cortex neurons were assessed by cross-correlation analysis of their responses to random ternary white noise. This stimulus consisted of multiple randomly placed bars, each colored white, black, or gray with equal probability, which were rerandomized every 5–10 ms. A first-order cross-correlation analysis of a neuron's spike train with the spatiotemporal history of the stimulus provided an estimate of the neuron's linear spatiotemporal filtering properties. A nonlinear correlation analysis measured the amount of interaction for pair-wise combinations of bars as a function of their relative spatial and temporal separations. The spatiotemporal orientation of each of these functions was quantified using a “motion energy index” (MEI), which was compared to the neurons' direction selectivity measured with drifting sinewave gratings. Both first-order and nonlinear correlation plots usually showed s–t orientation whose sign was consistent with the neuron's direction preference; however, in many cases the MEI for first-order analysis was weak compared to that seen in the nonlinear interactions. The structures of the nonlinear interaction functions were also compared with predictions from a conventional model of direction selectivity based on a simple spatiotemporally oriented linear filter, followed by an intensive nonlinearity (“LN model”). These comparisons showed that some neurons' data agreed reasonably well with such a model, while others agreed poorly or not at all. Simulations of an alternative model which combines signals from idealized lagged and nonlagged front-end linear filters produce noise correlation results more like those seen in the neurophysiological data.