Humans stand out among animals for their unique capacities in domains such as language, culture and imitation, but it is difficult to identify basic cognitive elements that are specifically human. In this talk, I will present evidence that, compared to humans, non-human animals have a more limited capacity to discriminate ordered sequences of stimuli. Collating data from over 100 experiments on stimulus sequence discrimination, I will show that animals commit pervasive and systematic errors, such as confusing a red–green sequence of lights with green–red and green–green sequences. These errors can persist after thousands of learning trials. Overall, the data are consistent with the assumption that non-human species represent stimulus sequences as unstructured collections of memory traces. This representation carries only approximate information about stimulus duration, recency, order, and frequency, yet it predicts non-human performance accurately. Lastly, I will present ongoing efforts to test sequence discrimination abilities in bonobos.