Ocular saccades bringing the gaze toward the straight-ahead direction (centripetal) exhibit higher dynamics than those steering the gaze away (centrifugal). This is generally explained by oculomotor determinants: centripetal saccades are more efficient because they pull the eyes back toward their primary orbital position. However, visual determinants might also be invoked: elements located straight-ahead trigger saccades more efficiently because they receive a privileged visual processing. Here, we addressed this issue by using both pro- and anti-saccade tasks in order to dissociate the centripetal/centrifugal directions of the saccades, from the straight-ahead/eccentric locations of the visual elements triggering those saccades. Twenty participants underwent alternating blocks of pro- and anti-saccades during which eye movements were recorded binocularly at 1 kHz. The results confirm that centripetal saccades are always executed faster than centrifugal ones, irrespective of whether the visual elements have straight-ahead or eccentric locations. However, by contrast, saccades triggered by elements located straight-ahead are consistently initiated more rapidly than those evoked by eccentric elements, irrespective of their centripetal or centrifugal direction. Importantly, this double dissociation reveals that the higher dynamics of centripetal pro-saccades stem from both oculomotor and visual determinants, which act respectively on the execution and initiation of ocular saccades.