Early in life, visual experience appears to influence the refinement and maintenance of the orientation-selective responses of neurons in the primary visual cortex. After eye opening, the statistical structure of visually driven neural responses depends not only on the stimulus, but also on how the stimulus is scanned during behavior. Modulations of neural activity due to behavior may thus play a role in the experience-dependent refinement of cell response characteristics. To investigate the possible influences of eye movements on the maturation of thalamocortical connectivity, we have simulated the responses of neuronal populations in the lateral geniculate nucleus (LGN) and V1 of the cat while images of natural scenes were scanned in a way that replicated the cat's oculomotor activity. In the model, fixational eye movements were essential to attenuate neural sensitivity to the broad correlational structure of natural visual input, decorrelate neural responses, and establish a regime of neural activity that was compatible with a Hebbian segregation of geniculate afferents to the cortex. We show that this result is highly robust and does not depend on the precise characteristics of the model.