We apply a computational model of biological motion processing [1,2] to a class of stimuli described by Taub et al [3]. In these, n translating sine waves, separated by 2pi/n radians but otherwise identical, are randomly sampled spatially to produce an nth order stimulus. For n > 1, the motion of these stimuli is non-Fourier. When n = 2 this non-Fourier motion is clearly visible to human observers. As n increases the direction discrimination threshold increases until, when n = 5, no reliable threshold can be measured [3]. We show that our computational model, an extension of the gradient approach, can accurately detect the direction of motion in the non-Fourier stimuli and that, as n increases, the accuracy with which the model detects the correct direction of motion is reduced. The modeling results concur with the psychophysical data. Importantly, the model, which acts directly on image luminance, detects non-Fourier motion without a preprocessing non-linearity (the hallmark of all other low-level approaches to the detection of non-Fourier motion). The most obvious explanation of how this might occur is that non-Fourier motion is specified by the spatiotemporal gradients within the motion sequences. We assess whether this is the case by measuring local spatial and temporal gradients and plotting these in the form of a gradient plot; a histogram where spatial gradient is shown on the x axis, temporal gradient on the y axis, and number of occurrences of spatial gradient/temporal gradient combinations is indicated on the z axis. This analysis shows that the gradients correctly indicating non-Fourier motion predominate within the stimuli when n = 2 and that this predominance reduces as n increases.