Just-noticeable differences (jnd's) in velocity were measured as a function of reference velocity for central and peripheral vision. The velocity discrimination curves plotting jnd's in velocity, expressed as Weber fractions, as a function of reference velocity were U shaped at all eccentricities. Under almost every stimulus condition the increase in jnd in velocity with increasing eccentricity was significantly larger at low reference velocities than at high reference velocities. Consequently the shift toward higher velocities with increasing eccentricity was much clearer for the lower end of the velocity-discrimination curve than for the upper end. These results are in agreement with the predictions derived from the response characteristics of velocity-tuned cells. Control experiments involving direction discrimination have shown that the impossibility of making fine velocity judgments at high speeds is due not to too weak a contrast for the stimulus motion to be visible but to a limitation in the neural apparatus analyzing velocity.