When animal behavior is studied in a laboratory environment, the animals are often extensively trained to shape their behavior. A crucial question is whether the behavior observed after training is part of the natural repertoire of the animal or represents an outlier in the animal’s natural capabilities. This can be investigated by assessing the extent to which the target behavior is manifested during the initial stages of training and the time course of learning. We explored this issue by examining smooth pursuit eye movements in monkeys naïve to smooth pursuit tasks. We recorded the eye movements of monkeys from the 1st days of training on a step-ramp paradigm. We used bright spots, monkey pictures and scrambled versions of the pictures as moving targets. We found that during the initial stages of training, the pursuit initiation was largest for the monkey pictures and in some direction conditions close to target velocity. When the pursuit initiation was large, the monkeys mostly continued to track the target with smooth pursuit movements while correcting for displacement errors with small saccades. Two weeks of training increased the pursuit eye velocity in all stimulus conditions, whereas further extensive training enhanced pursuit slightly more. The training decreased the coefficient of variation of the eye velocity. Anisotropies that grade pursuit across directions were observed from the 1st day of training and mostly persisted across training. Thus, smooth pursuit in the step-ramp paradigm appears to be part of the natural repertoire of monkeys’ behavior and training adjusts monkeys’ natural predisposed behavior.