We investigated how saccade target selection by humans and macaque monkeys reacts to unexpected changes of the image. This was explored using double step and search step tasks in which a target, presented alone or as a singleton in a visual search array, steps to a different location on infrequent, random trials. We report that human and macaque monkey performance are qualitatively indistinguishable. Performance is stochastic with the probability of producing a compensated saccade to the final target location decreasing with the delay of the step. Compensated saccades to the final target location are produced with latencies relative to the step that are comparable to or less than the average latency of saccades on trials with no target step. Noncompensated errors to the initial target location are produced with latencies less than the average latency of saccades on trials with no target step. Noncompensated saccades to the initial target location are followed by corrective saccades to the final target location following an intersaccade interval that decreases with the interval between the target step and the initiation of the noncompensated saccade. We show that this pattern of results cannot be accounted for by a race between two stochastically independent processes producing the saccade to the initial target location and another process producing the saccade to the final target location. However, performance can be accounted for by a race between three stochastically independent processes--a GO process producing the saccade to the initial target location, a STOP process interrupting that GO process, and another GO process producing the saccade to the final target location. Furthermore, if the STOP process and second GO process start at the same time, then the model can account for the incidence and latency of mid-flight corrections and rapid corrective saccades. This model provides a computational account of saccade production when the image changes unexpectedly.