In primate visual cortex (V1), about half the neurons are sensitive to the spatial phases of grating stimuli and generate highly modulated responses to drifting gratings (simple cells). The remaining cells show far less phase sensitivity and relatively unmodulated responses to moving gratings (complex cells). In the second visual area (V2) and the motion processing area MT (or V5), the majority of cells have unmodulated responses to drifting gratings - they are phase invariant. At just-detectable contrasts, 44% of V1 complex cells show highly modulated responses, but this contrast-dependent phase sensitivity is found in only 7% of V2 complex cells. We recorded from 149 cells in macaque MT - 142 classed as complex cells at high contrast. Approximately 14% (20/142) of MT complex cells showed significantly modulated responses to drifting gratings at just-detectable contrasts. A general feature of MT cells is that they can be divided into pattern and component selective types, but we found no correlation between this classification and contrast-dependent phase sensitivity. Phase sensitivity in MT is discussed in relation to MT's input structure.