We evaluated spatial displacement and temporal duration thresholds for discriminating the motion direction of gratings for a broad range of speeds (0.06 degrees/s to 30 degrees/s) in fovea and at +/-30 degrees eccentricity. In general, increased speed yielded lower duration thresholds but higher displacement thresholds. In most conditions, these effects of speed were comparable in fovea and periphery, yielding relatively similar thresholds not correlated with decreased peripheral acuity. The noteworthy exceptions were interactive effects at slow speeds: (1) Displacement thresholds for peripheral motion were affected by acuity limits for speeds below 0.5 degrees/s. (2) Low-vision observers with congenital nystagmus had elevated thresholds for peripheral motion and slow foveal motion but resembled typically sighted observers for foveal motions at speeds above 1 degree/s. (3) Suppressive center-surround interactions were absent below 0.5 degrees/s and their strength increased with speed. Overall, these results indicate qualitatively different sensitivities to slow and fast motions. Thresholds for very slow motion are limited by spatial resolution, while thresholds for fast motion are probably limited by temporal resolution.