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Humans routinely classify others according to both their individual attributes, such as social status or wealth, and membership in higher order groups, such as families or castes. They also recognize that people's individual attributes may be influenced and regulated by their group affiliations. It is not known whether such rule-governed, hierarchical classifications are specific to humans or might also occur in nonlinguistic species. Here we show that baboons recognize that a dominance hierarchy can be subdivided into family groups. In playback experiments, baboons respond more strongly to call sequences mimicking dominance rank reversals between families than within families, indicating that they classify others simultaneously according to both individual rank and kinship. The selective pressures imposed by complex societies may therefore have favored cognitive skills that constitute an evolutionary precursor to some components of human cognition.