Humans have the capacity to use stimuli interchangeably by forming equivalence classes, and this ability seems to be supported by our language system. According to Sidman and Tailby (Conditional discrimination vs. matching to sample: an expansion of the testing paradigm. J Exp Anal Behav 37:5-22, 1982), the formation of equivalence classes require that three relations are derived among the class members, and past experiments have shown that one of these relations, i.e., symmetry, corresponding to the ability to reverse a relation (if A -> B, then B -> A), is extremely difficult to obtain in non-human animals. Because language development and the ability to form equivalence classes both co-occur in children with an increased ability to form categories, the current study tested the idea that category learning might promote symmetry in a nonhuman primate species. In Experiment 1, twelve Guinea baboons (Papio papio) were trained to associate 60 pictures of bears and 60 pictures of cars to two category labels, before being tested in symmetry trials. In Experiment 2, symmetry was trained and tested by reversing the association order between labels and pictures, using a new set of stimuli. In both experiments, the baboons successfully demonstrated category discrimination, but had only a weak (though significant) tendency to respond in accordance with symmetry during test trials. Altogether, our results confirm that symmetry is inherently difficult in non-human animals. We discuss possible explanations for such a limitation and give reasons for thinking that the effects of categorization on symmetry should be further investigated.