Human language is a fundamentally cooperative enterprise, embodying fast-paced and extended social interactions. It has been suggested that it evolved as part of a larger adaptation of humans' species-unique forms of cooperation. Although our closest living relatives, bonobos and chimpanzees, show general cooperative abilities, their communicative interactions seem to lack the cooperative nature of human conversation. Here, we revisited this claim by conducting the first systematic comparison of communicative interactions in mother-infant dyads living in two different communities of bonobos (LuiKotale, DRC; Wamba, DRC) and chimpanzees (Taï South, Côte d'Ivoire; Kanyawara, Uganda) in the wild. Focusing on the communicative function of joint-travel-initiation, we applied parameters of conversation analysis to gestural exchanges between mothers and infants. Results showed that communicative exchanges in both species resemble cooperative turn-taking sequences in human conversation. While bonobos consistently addressed the recipient via gaze before signal initiation and used so-called overlapping responses, chimpanzees engaged in more extended negotiations, involving frequent response waiting and gestural sequences. Our results thus strengthen the hypothesis that interactional intelligence paved the way to the cooperative endeavour of human language and suggest that social matrices highly impact upon communication styles.