The perceived direction of a grating moving behind an elongated aperture is biased towards the aperture's long axis. This ``barber pole'' illusion is a consequence of integrating one-dimensional (1D) or grating and two-dimensional (2D) or terminator motion signals. In humans, we recorded the ocular following responses to this stimulus. Tracking was always initiated at ultra-short latencies (approximate to 85 ms) in the direction of grating motion. With elongated apertures, a later component was initiated 15-20 ms later in the direction of the terminator motion signals along the aperture's long axis. Amplitude of the later component was dependent upon the aperture's aspect ratio. Mean tracking direction at the end of the trial (135-175 ms after stimulus onset) was between the directions of the vector sum computed by integrating either terminator motion signals only or both grating and terminator motion signals. Introducing an elongated mask at the center of the ``barber pole'' did not affect the latency difference between early and later components, indicating that this latency shift was not due to foveal versus peripheral locations of 1D and 2D motion signals. Increasing the size of the foveal mask up to 90% of the stimulus area selectively reduced the strength of the grating motion signals and, consequently, the amplitude of the early component. Conversely, reducing the contrast of, or indenting the aperture's edges, selectively reduced the strength of terminator motion signals and, consequently, the amplitude of the later component. Latencies were never affected by these manipulations. These results tease apart an early component of tracking responses, driven by the grating motion signals and a later component, driven by the line-endings moving at the intersection between grating and aperture's borders. These results support the hypothesis of a parallel processing of 1D and 2D motion signals with different temporal dynamics.