Before initiating a saccade to a moving target, the brain must take into account the target's eccentricity as well as its movement direction and speed. We tested how the kinematic characteristics of the target influence the time course of this oculomotor response. Participants performed a step-ramp task in which the target object stepped from a central to an eccentric position and moved at constant velocity either to the fixation position (foveopetal) or further to the periphery (foveofugal). The step size and target speed were varied. Of particular interest were trials that exhibited an initial saccade prior to a smooth pursuit eye movement. Measured saccade reaction times were longer in the foveopetal than in the foveofugal condition. In the foveopetal (but not the foveofugal) condition, the occurrence of an initial saccade, its reaction time as well as the strength of the pre-saccadic pursuit response depended on both the target's speed and the step size. A common explanation for these results may be found in the neural mechanisms that select between oculomotor response alternatives, i.e., a saccadic or smooth response.