Comparative studies between human and nonhuman primates concerning communicative behaviors and its brain specialization know a renewed interest regarding the evolution of language. In the present communication, I will first report the elaboration of novel gestures in the repertoire of some individuals in olive baboons Papio anubis housed in at the Station de Primatologie CNRS in France (such as « clapping », « cage bagging » and « food presenting ») that have never been observed in other conspecifics. Second, I will focus particularly on “Food presenting” gesture which has been described in one single female. Her behavior consists of trying to redirect the attention of the offspring toward an external object (i.e. food) by engaging mutual gaze when agitating manually the object toward the offspring’s face. From the observations of these mother-infant interactions across 4 births from 2009 to 2015 as well as video coding of 11 gestures sequences, I will show that this behavior (1) occurred toward every offspring and finally stopped when were able to feed themselves; (2) fit all criteria of intentional communication and joint attention, namely recipient-directed, mutual gaze, signal persistence including systematic mother’s readjustments (moves, posture, head, gaze and manual gesture orientations) for maintaining both mutual gaze and the “food presenting” gesture’s orientation toward the offspring’s face when the offspring moves away. Finally, thanks to anatomical in vivo cerebral images collected by MRI in 100 adults and 34 new-born baboons, I will show communicative gesturing in baboons might be related to early language-homolog brain asymmetry. I will discuss the theoretical implications of those collective finding regarding evolution of social cognition, declarative communication, language and its brain specialization.