Combinatorial semantics is a core property of human language whose mechanisms remain poorly known. This study used computerized tasks with touch screens to investigate whether baboons (Papio papio) can understand the combination of shape and color labels in order to designate their corresponding colored shape. The baboons were trained either directly with label-pairs (Experiment 1) or with individual shape and color labels (Experiment 2), before being tested with novel compound labels from which they had to identify the referent. Compound labels understanding was found in one out of seven baboons tested in Experiment 1. Quite surprisingly, none of the 11 baboons showed this capacity in Experiment 2. We discuss several aspects of our protocols which could explain this difference between our two experiments, as well as the significance of our findings for language studies in animals and children. (C) 2015 Elsevier B.V. All rights reserved.