Interfemale competition regimes in primate societies have been described as despotic or egalitarian based on female social behaviour. Hierarchies and nepotism are typical of despotic primates, where dominance rank and kinship are known to be strong drivers of who grooms whom and who fights with whom. However, a general theory for what structures female–female interactions in egalitarian societies remains underdeveloped. We present two nonmutually exclusive hypotheses that each propose a mechanism for levelling social advantages in a group by conferring social favour to all or most females over time: transitory states (age, residency status and reproductive state) bias social interactions and/or reciprocity governs social interactions. In this study, we (1) determined that a group of red colobus monkeys, Procolobus rufomitratus tephrosceles, in Kibale National Park, Uganda, are highly egalitarian; (2) tested our hypotheses for how egalitarianism may be maintained in this group; and (3) analysed findings across primate studies for support for either hypothesis. In red colobus, agonistic interactions were predicted by age – a transitory state – and transitory states and reciprocity predicted grooming interactions: avid groomers, older females and short-term resident females received more grooming. In addition, behavioural indicators of social status (aggression given and grooming received) were not associated with reproductive success in red colobus, as might be expected in an egalitarian group where variance in fitness should be low. Across primates, we found that transitory states commonly structure social interactions in egalitarian societies but not in despotic societies and that reciprocity is highly variable, especially among egalitarian societies. Rotating social advantage as females shift among transitory states and/or reciprocate grooming may lower interfemale skew in social benefits and potentially in lifetime reproductive success in egalitarian groups, setting them apart from despotic societies where dominance hierarchies and kinship maintain a more static and unequal distribution of social advantage.