Primates (including humans) heavily rely on the efficiency of their visual system which, contrary to man-made cameras, exploits parallel channels conveying qualitatively different signals with graded precision depending on the eccentricity of objects in the visual field and with different dynamics. The interactions with the visual environment involve selecting and focusing on targets or areas of interest, actively and continuously sampling local information, instead of contemplating a homogeneous visual flow. Eye movements are a specific case of these actions, allowing to foveate targets and track their motion. Once the target is captured in the fovea, these movements are usually classified into catch-up saccades (with the eye rapidly jumping from one orientation – or fixation – to another) and smooth pursuit (with the eye continuously tracking a target with low velocity). Recent results in the monkey show a reduction in the number of catch-up saccades and an increase of smooth pursuit velocity when a moving target is repeatedly observed and tracked [1]. The mechanisms underlying this learning permit the maintenance of the target within in the central visual field at its current (here-and-now) location, despite the delays involved in processing visual signals. Here, we model such transitions and sustained oculomotor response using dynamic neural fields, extending previous models by incorporating actions and activity propagation into the dynamical equations ruling the estimation of current target position [2]. Such estimated position is then used to trigger eye movements, either taking the form of pursuit slow eye movement or a catch-up saccade depending on the location and the dynamical characteristics of activity in the neural field. Propagation of activity in various directions thus compete for action at all times, leading to qualitatively different behaviors: 1) fixations and fixational eye movements due to small variations in the weight of opposite propagations when the target is stationary, 2) intercepting or catch-up saccades when activity peaks alternatively build and relax on the neural field (e.g. when the target moves at a high but unknown velocity), 3) slow eye movement when the activity peak drifts and follows the target movement, 4) pursuit eye movements compensating for lags or change in direction when the target trajectory is learned. Therefore, smoothly pursuing a foveated moving target here simply corresponds to stable attractors in the dynamical oculomotor system, adopting a sensorimotor and interactive view of the visual system. Such stable attractors only appear once learning has extracted the regularities of target trajectories.