Gaze following, the ability to follow the gaze of other individuals, has been widely studied in non-human primate species, mostly in adult individuals. Yet, the literature on gaze following revealed a quite variability across the different findings, some of it might reflect true inter-species differences, while others might be related to methodological differences, or to an underestimation of the factors involved in the expression of gaze following. In the current study, we tested 54 captive olive baboons (Papio anubis), housed in social groups, to assess how juvenile and adult baboons would spontaneously react to a sudden change in the direction of a human experimenter's head. First, our results showed that juveniles, more than adult baboons, co-oriented their gaze with the experimenter's gaze. We also observed a strong habituation effect in adult baboons but not in juveniles, as the adults' response vanished at the second exposure to a change of direction of the experimenter's head. Second, our results showed that juveniles subsequently adopted an original strategy when the experimenter's head indicated some new directions: they reliably adjusted their spatial body position to keep a gaze contact with the experimenter's line of sight. We discussed how the age class and the individual expertise of the baboons could lead to some modulations in terms of attentiveness, motivation, or cognitive abilities, and thus likely influence gaze following.