The ability to track syntactic relationships between words, particularly over distances (“nonadjacent dependencies”), is a critical faculty underpinning human language, although its evolutionary origins remain poorly understood. While some monkey species are reported to process auditory nonadjacent dependencies, comparative data from apes are missing, complicating inferences regarding shared ancestry. Here, we examined nonadjacent dependency processing in common marmosets, chimpanzees, and humans using “artificial grammars”: strings of arbitrary acoustic stimuli composed of adjacent (nonhumans) or nonadjacent (all species) dependencies. Individuals from each species (i) generalized the grammars to novel stimuli and (ii) detected grammatical violations, indicating that they processed the dependencies between constituent elements. Furthermore, there was no difference between marmosets and chimpanzees in their sensitivity to nonadjacent dependencies. These notable similarities between monkeys, apes, and humans indicate that nonadjacent dependency processing, a crucial cognitive facilitator of language, is an ancestral trait that evolved at least ~40 million years before language itself.