During natural vision, humans make frequent eye movements but perceive a stable visual world. It is therefore likely that the human visual system contains representations of the visual world that are invariant to eye movements. Here we present an experiment designed to identify visual areas that might contain eye-movement-invariant representations. We used functional MRI to record brain activity from four human subjects who watched natural movies. In one condition subjects were required to fixate steadily, and in the other they were allowed to freely make voluntary eye movements. The movies used in each condition were identical. We reasoned that the brain activity recorded in a visual area that is invariant to eye movement should be similar under fixation and free viewing conditions. In contrast, activity in a visual area that is sensitive to eye movement should differ between fixation and free viewing. We therefore measured the similarity of brain activity across repeated presentations of the same movie within the fixation condition, and separately between the fixation and free viewing conditions. The ratio of these measures was used to determine which brain areas are most likely to contain eye movement-invariant representations. We found that voxels located in early visual areas are strongly affected by eye movements, while voxels in ventral temporal areas are only weakly affected by eye movements. These results suggest that the ventral temporal visual areas contain a stable representation of the visual world that is invariant to eye movements made during natural vision.