Gestural communication is a modality considered in the literature as a candidate for determining the ancestral prerequisites of the emergence of human language. As reported in captive chimpanzees and human children, a study in captive baboons revealed that a communicative gesture elicits stronger degree of right-hand bias than non-communicative actions. It remains unclear if it is the communicative nature of this manual behavior which induces such patterns of handedness. In the present study, we have measured hand use for two uninvestigated behaviors in a group of captive olive baboons: (1) a non-communicative self-touching behavior ("muzzle wipe" serving as a control behavior), (2) another communicative gesture (a ritualized "food beg") different from the one previously studied in the literature (a species-specific threat gesture, namely "hand slap") in the same population of baboons. The hand preferences for the "food beg" gestures revealed a trend toward right-handedness and significantly correlated with the hand preferences previously reported in the hand slap gesture within the same baboons. By contrast, the hand preferences for the self-touching behaviors did not reveal any trend of manual bias at a group-level nor correlation with the hand preferences of any communicative gestures. These findings provide additional support to the hypothesized existence in baboons of a specific communicative system involved in the production of communicative gestures that may tend to a left-hemispheric dominance and that may differ from the system involved in purely motor functions. The hypothetical implications of these collective results are discussed within the theoretical framework about the origins of hemispheric specialization for human language. (Contains 2 figures.)