Two types of central nervous system integrators are critical for oculomotor performance. The first integrates velocity commands to create position signals that hold fixation of the eye. The second stores relative velocity of the head and visual surround to stabilize gaze both during and after the occurrence of continuous self and world motion. We have used recordings from single neurons to establish that the "position" and "velocity" integrators for horizontal eye movement occupy adjacent, but nonoverlapping, locations in the goldfish medulla. Lidocaine inactivation of each integrator results in the eye movement deficits expected if horizontal eye position and velocity signals are processed separately. These observations also indicate that each brainstem compartment generates and stores these signals. Consequently, each integrator exhibits functional autonomy. Therefore, we propose that the intrinsic electrophysiological properties of the constituent neurons in each brainstem subnucleus may be sufficient for producing integrator rhythmicity.