Sequential learning plays a role in a variety of common tasks, such as huma
n language processing, animal communication, and the learning of action seq
uences. In this article, we investigate sequential learning in non-human pr
imates from a comparative perspective, focusing on three areas: the learnin
g of arbitrary, fixed sequences; statistical learning; and the learning of
hierarchical structure. Although primates exhibit many similarities to huma
ns in their performance on sequence learning tasks, there are also importan
t differences. Crucially, non-human primates appear to be limited in their
ability to learn and represent the hierarchical structure of sequences. We
consider the evolutionary implications of these differences and suggest tha
t limitations in sequential learning may help explain why non-human primate
s lack human-like language.