It is commonly acknowledged that gamma-band oscillations arise from interplay between neural excitation and inhibition; however, the neural mechanisms controlling the power of stimulus-induced gamma responses (GR) in the human brain remain poorly understood. A moderate increase in velocity of drifting gratings results in GR power enhancement, while increasing the velocity beyond some 'transition point' leads to GR power attenuation. We tested two alternative explanations for this nonlinear input-output dependency in the GR power. First, the GR power can be maximal at the preferable velocity/temporal frequency of motion-sensitive V1 neurons. This 'velocity tuning' hypothesis predicts that lowering contrast either will not affect the transition point or shift it to a lower velocity. Second, the GR power attenuation at high velocities of visual motion can be caused by changes in excitation/inhibition balance with increasing excitatory drive. Since contrast and velocity both add to excitatory drive, this 'excitatory drive' hypothesis predicts that the 'transition point' for lowcontrast gratings would be reached at a higher velocity, as compared to high-contrast gratings. To test these alternatives, we recorded magnetoencephalography during presentation of low (50%) and high (100%) contrast gratings drifting at four velocities. We found that lowering contrast led to a highly reliable shift of the GR suppression transition point to higher velocities, thus supporting the excitatory drive hypothesis. No effects of contrast or velocity were found in the alpha-beta range. The results have implications for understanding the mechanisms of gamma oscillations and developing gamma-based biomarkers of disturbed excitation/inhibition balance in brain disorders.