When an object moves in the visual field, its motion evokes a streak of activity on the retina and the incoming retinal signals lead to robust oculomotor commands because corrections are observed if the trajectory of the interceptive saccade is perturbed by a microstimulation in the superior colliculus. The present study complements a previous perturbation study by investigating, in the head-restrained monkey, the generation of saccades toward a transient moving target (100–200 ms). We tested whether the saccades land on the average of antecedent target positions or beyond the location where the target disappeared. Using target motions with different speed profiles, we also examined the sensitivity of the process that converts time-varying retinal signals into saccadic oculomotor commands. The results show that, for identical overall target displacements on the visual display, saccades toward a faster target land beyond the endpoint of saccades toward a target moving slower. The rate of change in speed matters in the visuomotor transformation. Indeed, in response to identical overall target displacements and durations, the saccades have smaller amplitude when they are made in response to an accelerating target than to a decelerating one. Moreover, the motion-related signals have different weights depending upon their timing relative to the target onset: early signals are more influential in the specification of saccade amplitude than later signals. We discuss the “predictive” properties of the visuo-saccadic system and the nature of this location where the saccades land, after providing some critical comments to the “hic-et-nunc” hypothesis (Fleuriet and Goffart, 2012).