The present paper focuses on a classic hyperacuity, Vernier acuity-the ability to discriminate breaks in the collinearity of lines or edges on the order of only arcseconds of visual angle. We measured steady-state sweep visual evoked potentials (sVEPs) in response to 6 Hz periodic breaks in collinearity (Vernier offsets) in horizontal squarewave gratings. Vernier thresholds, estimated by extrapolating the amplitude of the first harmonic (1F) to 0 µV, were measured for gratings with 4%, 8%, 16%, 32%, 64%, and 80% contrast, with gaps of 0, 2, or 5 arcmin introduced between neighboring bar elements that formed the Vernier offsets. Thresholds for the 2F response component provided an estimate of motion thresholds. The data confirmed and extended evidence that the odd- and even-harmonic components reflect cortical activity of different neurons (i.e., neurons that respond asymmetrically to the periodic breaks in alignment and neurons that respond symmetrically to the local relative motion cue of the stimulus). Suprathreshold data (peak amplitude, response slope, and response phase at the peak amplitude) provided additional independent evidence of this notion. Vernier thresholds decreased linearly as contrast increased, with a slope of approximately -0.5 on log-log axes, similar to prior psychophysical results. The form of contrast dependence showed more similarity to measures of magnocellular ganglion cell spatial precision than measures from parvocellular ganglion cells. Our data thus support the hypothesis that magnocellular ganglion cell output from the retina has the requisite properties to support cortical calculation of Vernier offsets at a hyperacuity level.