Two types of eye movement are made while one tracks a target moving in the visual field. The first type is an abrupt step-like movement (called saccade) that rapidly rotates the eyes toward the target location and brings its image within the central visual field. The second type is a slower movement (called pursuit) whose velocity approximates that of the target. From the retinal excitation to the contraction of extraocular muscle fibers, distinct and parallel visuomotor channels are involved in generating these two movements. Most of the time, the eyes do not rotate as fast as the target; the target image slips on the retina and catch-up saccades punctuate the oculomotor tracking. The performance during which gaze moves continuously and as fast as the target is not spontaneous but requires training. During the last six decades, numerous studies investigated the neuronal processes driving the changes in the orientation of the eyes in response to a moving target. High-resolution recording techniques yielded time series of numerical values from which magnitudes such as eye movement amplitude, duration and velocity were calculated. Some models proposed the existence in the brain of processes that would reduce the difference between internal signals encoding gaze and target directions (for guiding the saccade) and the difference between signals encoding the eye rotation speed and the target speed (for accelerating the slow pursuit component). Lastly, during the pursuit maintenance, a process would sustain the eye velocity while the target image is more or less stabilized in the central visual field. This cybernetic formalism guided electrophysiologists who studied the correlations between the activity of neurons and various kinematic parameters of the eyes and target (position, distance, amplitude, velocity and even acceleration). A one-to-one correspondence was often assumed between notions belonging to the physical world and the inner functioning of the brain. However, contrary to the receptacle (space) within which the object is moving, the brain medium is not empty, neutral, homogeneous, isotropic or uniform. The neurophysiology unravels clusters of various kinds of cells between which multiple channels transmit the retinal signals with unequal conduction speeds. Before converging onto the motor nerves and exciting the appropriate muscle fibers, the visuomotor transmission consists of flows of activity that are distributed across several neuronal regions. Within these neuronal networks, the neural image of a small target spot does not look compact and rigid but dynamic and expanded, spatially and temporally. Yet, despite this tremendous complexity, animals exhibit the ability to capture an object, at the location where it is and at the time when it is there. During my communication, I shall report examples illustrating attempts to “cerebralize” kinematic parameters and explain their limitations. Instead of embedding within the cerebral medium, notions that are classically used to describe the motion of a rigid body in the external world, an alternative option remains possible. A saccade can be viewed as the outcome of a process that restores an equilibrium between visuomotor channels exerting mutually opposing tendencies whereas the slow eye movement as a sustained imbalance.