When generating a saccade toward a moving target, the target displacement that occurs during the period spanning from its detection to the saccade end must be taken into account to accurately foveate the target and to initiate its pursuit. Previous studies have shown that these saccades are characterized by a lower peak velocity and a prolonged deceleration phase. In some cases, a second peak eye velocity appears during the deceleration phase, presumably reflecting the late influence of a mechanism that compensates for the target displacement occurring before saccade end. The goal of this work was to further determine in the head restrained monkey the dynamics of this putative compensatory mechanism. A step-ramp paradigm, where the target motion was orthogonal to a target step occurring along the primary axes, was used to estimate from the generated saccades: a component induced by the target step and another one induced by the target motion. Resulting oblique saccades were compared with saccades to a static target with matched horizontal and vertical amplitudes. This study permitted to estimate the time taken for visual motion-related signals to update the programming and execution of saccades. The amplitude of the motion-related component was slightly hypometric with an undershoot that increased with target speed. Moreover, it matched with the eccentricity that the target had 40–60 ms before saccade end. The lack of significant difference in the delay between the onsets of the horizontal and vertical components between saccades directed toward a static target and those aimed at a moving target questions the late influence of the compensatory mechanism. The results are discussed within the framework of the “dual drive” and “remapping” hypotheses.