Visual response properties of retinal ganglion cells (GCs), the retinal output neurons, are shaped by numerous processes and interactions within the retina. In particular, amacrine cells are known to form microcircuits that affect GC responses in specific ways. So far, relatively little is known about the influence of retinal processing on GC responses under naturalistic viewing conditions, in particular in the presence of fixational eye movements. Here we used a detailed model of the mammalian retina to investigate possible effects of fixational eye movements on retinal GC activity. Populations of linear, sustained (parvocellular, PC) and nonlinear, transient (magnocellular, MC) GCs were simulated during fixation of a star-shaped stimulus, and two distinct effects were found: (1) a fading of complete wedges of the star and (2) an apparent splitting of stimulus lines. Both effects only occur in MC-cells, and an analysis shows that fading is caused by an expression of the aperture problem in retinal GCs, and the splitting effect by spatiotemporal nonlinearities in the MC-cell receptive field. These effects strongly resemble perceived instabilities during fixation of the same stimulus, and we propose that these illusions may have a retinal origin. We further suggest that in this case two parallel retinal streams send conflicting, rather than complementary, information to the higher visual system, which here leads to a dominant influence of the MC pathway. Similar situations may be common during natural vision, since retinal processing involves numerous nonlinearities.