The saccadic and vergence systems were considered independent in the past. Combined saccade-vergence movement can be viewed through the resultant trajectories of the binocular fixation point, which were originally described by Yarbus for motion in the horizontal plane of regard. According to Yarbus, pure conjugate saccades are performed along iso-vergence arcs; saccade-vergence co-action results in triphasic trajectories --- the first and last being along iso-version lines and the intermediate one comprising the superposition of conjugate and disjunctive motion. This classical picture has been revised and updated, subsequent research revealing that the two systems are intertwined. In particular, we know now that even supposedly conjugate saccades are accompanied by intrinsic disjunctive motion. This phenomenon can be explained by peripheral mechanisms although its real cause is yet unknown and it could be central. Another aspect of the interaction is the speeding or facilitation of disjunctive movement by saccades. Furthermore, an asymmetry has been observed between converging and diverging motion.

The studies of the last decade have led, in effect, to the abandonment of the triphasic Yarbus scheme. Recently, Collewijn and his colleagues (1997, Vision Research, 37(8): 1049-1069) examined saccade-vergence interaction as reflected in binocular fixation point trajectories in the horizontal plane of regard. They observed vergence motion along iso-version lines at the initial and final portions of non-conjugate saccadic movement, thereby partially recovering the triphasic model. Moreover, the amount of vergence achieved before the start of a saccade increases together with the ratio of required vergence relative to the size of conjugate motion. This is indicative of a common timing mechanism for the two systems.

The most elaborate and successful model to date of saccade-vergence interaction is the dynamic model proposed by Zee et al. (1992, J. Neurophys., 68(5): 1624-1641). However, the model does not address the existence of initial pure vergence motion and the pattern of temporal co-ordination. Also, the reported results are presented in ocular angle co-ordinates which are difficult to compare with data of fixation point trajectories.

In order to overcome these shortcomings, we construct a simple kinematic model that is intended to reproduce the main features seen in fixation point trajectories. The basic building blocks of the model are smooth binocular velocity functions that can be interpreted as the actual velocity of the eyes or as the activity in motoneuron pools. Each such velocity function is a bell-shaped Gaussian, in conjugate or disjunctive co-ordinates. The model provides a parsimonious representation of a variety of trajectories. In addition, it touches upon the current controversy as to whether saccade control is essentially binocular or monocular.