We used one-dimensional sparse noise stimuli to generate first-order spatiotemporal maps and second-order two-bar interaction maps for 65 simple and 124 complex direction-selective cells in alert macaque V1. Spatial and temporal phase differences between light and dark space-time maps clearly distinguished simple and complex cell populations. Complex cells usually showed similar direction preferences to light and dark bars, but many of the directional simple cells were much more direction selective to one sign of contrast than the reverse. We show that this is predicted by a simple energy model. Some of the direction-selective simple cells showed multiple space-time-slanted subregions, but others (previously described as S1 cells) had space-time maps that looked like just one subregion of an ordinary simple cell. Both simple and complex cells showed directional interactions (nonlinearities) to pairs of flashed bars (a 2-bar apparent-motion stimulus). The space-time slant of the simple cells correlated with the optimum dX/dT (velocity) of the paired-bar interactions. Some complex cells also showed a space-time slant; the direction of the slant usually correlated with the preferred direction of motion, but the degree of slant correlated with the inferred velocity tuning only when measured by a weighted-centroid calculation. Principal components analysis of the simple-cell space-time maps yielded one fast temporally biphasic component and a slower temporally monophasic component. We saw no consistent pattern for the spatial phase of the components, unlike previous reports; however, we show that principal components analysis may not distinguish between spatial offsets and phase offsets.