Displacement thresholds for continuous oscillatory movement of a grating, subtending 2 cycle deg-1, were measured for square-, triangular- and sine-wave oscillation over the frequency range 1-20 Hz. Without reference lines, thresholds were highly dependent upon temporal frequency and oscillation waveform. With reference lines, thresholds were dependent upon oscillation waveform but not frequency. Greatest sensitivity was shown to square-wave oscillation and least to triangular-wave. Results are discussed in terms of velocity- and displacement-analysing systems. Increasing the spatial frequency of the sinusoidally oscillating grating had little effect on displacement thresholds.