Previous work has shown that a single dot moving in a consistent direction is easily detected among noise dots in Brownian motion (Watamaniuk et al., Vis Res 1995;35:65-77). In this study we calculated the predictions of a commonly-used psychophysical motion model for a motion trajectory in noise. This model assumes local motion energy detectors optimally tuned to the signal, followed by a decision stage that implements the maximum rule. We first show that local motion detectors do indeed explain the detectability of brief trajectories (100 ms) that fall within a single unit, but that they severely underestimate the detectability of extended trajectories that span multiple units. For instance, a 200 ms trajectory is approximately three times more detectable than two isolated 100 ms trajectories presented together within an equivalent temporal interval. This result suggests a nonlinear interaction among local motion units. This interaction is not restricted to linear trajectories because circular trajectories with curvatures larger than 1 degree are almost as detectable as linear trajectories. Our data are consistent with a flexible network that feeds forward excitation among units tuned to similar directions of motion.