We investigated the capacity of 6 humans to make voluntary smooth eye movements with a horizontally stabilized foveal point target. When the target was viewed on a dark field, all subjects were able to make smooth oscillatory eye movements when they attempted to imitate their own normal pursuit of sinusoidal target movement (0.2-0.7 Hz) directly preceding the stabilization on the fovea. The frequency of the imitating eye movement was in general lower than the frequency of normal pursuit by 2-35%. While fixating a foveally stabilized point target superimposed on a large, sinusoidally moving non-stabilized background, all subjects were able to make either no eye movements, eye movements nearly in phase with or eye movements nearly in counterphase with the background movement depending on the instruction to imagine the target as head-stationary, moving in phase, or moving in counterphase with the background. The accuracy of the frequency of the smooth eye movement with the stabilized target on the moving background was higher than during imitation of pursuit on the dark field but the precision of the frequency was lower than during normal pursuit. When the background moved pseudo-randomly all subjects could voluntarily inhibit their smooth eye movements or could make smooth eye movements in phase with the background. Only 2 subjects showed a limited ability to make smooth eye movements opposite to the pseudo-random background movement. The results suggest that with predictable background movement the volition of the subject rather than the movement of the background determines the eye movements when the subject looks at the foveally stabilized target.