Abstract: The tendency in primate groups for two opponents to affiliate shortly after a fight has been described as dyadic reconciliation. The response has been shown to restore disrupted relationships and curtail ongoing aggression. Rates of self-directed behaviour (e.g. scratching) are positively correlated with anxiety in primates and the rates decline after reconciliation, indicating that the response also functions to reduce postconflict tension. Third parties not involved in an aggressive interaction are also likely to affiliate with one of the combatants subsequent to a fight. Such `triadic' interactions may also promote conflict resolution when, for instance, the relatives of a victim affiliate with their relative's aggressor. Because aggression in a group influences a bystander's behaviour with combatants, we hypothesized that aggression between two animals would also influence a bystander's behaviour with other bystanders. Such `quadratic' postconflict interactions might also function to reduce postconflict tension or occur in patterns among kin subgroups to resolve conflict. We tested for quadratic interactions in an 18-member group of captive hamadryas baboons, Papio hamadryas hamadryas. Immediately following a fight, an uninvolved bystander was randomly selected for observation and its affiliative interactions with other bystanders and its displacement activities were recorded for 3 min. Rates of behaviour during these postconflict periods were compared to rates during 3-min baseline periods not preceded by aggression. Bystanders engaged in quadratic interactions by increasing affiliation with other bystanders following aggression. Bystanders directed affiliation to nonkin bystanders that were their preferred social partners. Displacement activities of bystanders were significantly higher during postconflict intervals compared to baseline intervals, and bystander displacement activity levels before affiliative contact with other bystanders were significantly higher than after contact. Apparently, bystanders become tense or anxious after witnessing aggression and affiliate with preferred partners to reduce the arousal.