Human language, and grammatical competence in particular, relies on a set of computational operations that, in its entirety, is not observed in other animals. Such uniqueness leaves open the possibility that components of our linguistic competence are shared with other animals, having evolved for non-linguistic functions. Here, we explore this problem from a comparative perspective, asking whether cotton-top tamarin monkeys (Saguinus oedipus) can spontaneously (no training) acquire an affixation rule that shares important properties with our inflectional morphology (e.g. the rule that adds –ed to create the past tense, as in the transformation of walk into walk-ed). Using playback experiments, we show that tamarins discriminate between bisyllabic items that start with a specific ‘prefix’ syllable and those that end with the same syllable as a ‘suffix’. These results suggest that some of the computational mechanisms subserving affixation in a diversity of languages are shared with other animals, relying on basic perceptual or memory primitives that evolved for non-linguistic functions.