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It is generally assumed that the perception of non-Fourier motion requires the operation of some nonlinearity before motion analysis. We apply a computational model of biological motion processing to a class of non-Fourier motion stimuli designed to investigate nonlinearity in human visual processing. The model correctly detects direction of motion in these non-Fourier stimuli without recourse to any preprocessing nonlinearity. This demonstrates that the non-Fourier motion in some non-Fourier stimuli is directly available to luminance-based motion mechanisms operating on measurements of local spatial and temporal gradients.