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When multiple competing visual stimuli are present, saccades show more trajectory variations than those produced by single-target stimuli. In particular, variable trajectories including curved and averaging saccades are observed when visual search is required to select and make a saccade to a target. In this paper, based on our behavioral observations and neural recordings in the superior colliculus (SC) in monkeys, we propose a new, distributed SC and cerebellum (CBM) model that accounts for the saccade trajectory variations produced by the presence of multiple visual stimuli. The long-range lateral inhibitory connections between SC units are replaced by local excitatory connections and short-range inhibition. The inhibition to the SC from the substantia nigra (SNr) is assumed to have distributed spatial tuning. The interactions between visually activated populations of SC units and the distributed SNr inhibition produce variable initial directions of saccadic trajectories and these directional variations are partially compensated by the CBM feedback system.