Human and non-human primates share the ability to extract adjacent dependencies and, under certain conditions, non-adjacent dependencies (i.e., predictive relationships between elements that are separated by one or several intervening elements in a sequence). In this study, we explore the online extraction dynamics of non-adjacent dependencies in humans and baboons using a serial reaction time task. Participants had to produce three-target sequences containing deterministic relationships between the first and last target locations. In Experiment 1, participants from the two species could extract these non-adjacent dependencies, but humans required less exposure than baboons. In Experiment 2, the data show for the first time in a non-human primate species the successful generalization of sequential non-adjacent dependencies over novel intervening items. These findings provide new evidence to further constrain current theories about the nature and the evolutionary origins of the learning mechanisms allowing the extraction of non-adjacent dependencies.