Oculomotor tracking of moving objects is an important component of visually based cognition and planning. Such tracking is achieved by a combination of saccades and smooth-pursuit eye movements. In particular, the saccadic and smooth-pursuit systems interact to often choose the same target, and to maximize its visibility through time. How do multiple brain regions interact, including frontal cortical areas, to decide the choice of a target among several competing moving stimuli? How is target selection information that is created by a bias (e.g., electrical stimulation) transferred from one movement system to another? These saccade-pursuit interactions are clarified by a new computational neural model, which describes interactions between motion processing areas: the middle temporal area, the middle superior temporal area, the frontal pursuit area, and the dorsal lateral pontine nucleus; saccade specification, selection, and planning areas: the lateral intraparietal area, the frontal eye fields, the substantia nigra pars reticulata, and the superior colliculus; the saccadic generator in the brain stem; and the cerebellum. Model simulations explain a broad range of neuroanatomical and neurophysiological data. These results are in contrast with the simplest parallel model with no interactions between saccades and pursuit other than common-target selection and recruitment of shared motoneurons. Actual tracking episodes in primates reveal multiple systematic deviations from predictions of the simplest parallel model, which are explained by the current model.