The medial superior temporal area (MST) contains neurons with tuning for complex motion patterns, but very little is known about the generation of such responses. To explore how neuronal responses varied across complex motion pattern coherence, we recorded from single units while varying the strength of the global motion pattern in random dot stimuli. Stimuli were a family of optic flow patterns, consisting of radial motion, rotary motion, or combinations thereof ('spiral space'). We controlled the strength of the motion in the stimuli by varying the coherence -- the proportion of dots carrying the signal. This allows motion strength to be varied independently of stimulus size, speed, or contrast. Most neurons' responses were well described as a linear function of stimulus coherence. While more than half the cells possessed significant nonlinearities, these typically accounted for little additional variance. Nonlinear coherence response functions could either be compressive (e.g. saturating) or expansive, and occurred in both the preferred and null direction responses. The presence of nonlinearities was not related to neuronal response properties such as preferred spiral-space direction or tuning bandwidth; however, cells with compressive nonlinearities in both the preferred and null directions tended to have higher response amplitudes and were more sensitive to weak motion signals. These cells did not appear to form a distinct subpopulation within MST. Our results suggest that MST neurons predominantly linearly encode increasing pattern motion energy within their RFs.