The origin of human speech is still a hotly debated topic in science. Evidence of socially-guided acoustic flexibility and proto-conversational rules has been found in several monkey species, but is lacking in social and cooperative great apes. Here we investigated spontaneous vocal interactions within a peaceful context in captive bonobos to reveal that vocal interactions obey temporally and social rules. Dyadic vocal interactions were characterized by call overlap avoidance and short inter-call intervals. Bonobos preferentially responded to conspecifics with whom they maintained close bonds. We also found that vocal sharing rate (production rate of shared acoustic variants within each given dyad) was mostly explained by the age difference of callers, as other individual characteristics (sex, kinship) and social parameters (affinity in spatial proximity and in vocal interactions) were not. Our results show that great apes spontaneously display primitive conversation rules guided by social bonds. The demonstration that such coordinated vocal interactions are shared between monkeys, apes and humans fills a significant gap in our knowledge of vocal communication within the primate phylogeny and highlights the universal feature of social influence in vocal interactions.