Neurons in visual areas of the brain are generally characterized by the increase in firing rate that occurs when a stimulus is flashed on in the receptive field (RF). However, neurons also increase their firing rate when a stimulus is turned off. These “termination responses” or “after-discharges” that occur with flashed stimuli have been observed in area V1 and they may be important for vision as stimulus terminations have been shown to influence visual perception. The goal of the present study was to determine the strength of termination responses in the more natural situation in which eye movements move a stimulus out of an RF. We find that termination responses do occur in macaque V1 when termination results from a saccadic eye movement, but they are smaller in amplitude compared to flashed-off stimuli. Furthermore, there are termination responses even in the absence of visual stimulation. These findings demonstrate that termination responses are a component of naturalistic vision. They appear to be based on both visual and nonvisual signals in visual cortex. We speculate that the weakening of termination responses might be a neural correlate of saccadic suppression, the loss of perceptual sensitivity around the time of saccades.