Great ape cognition is used as a reference point to specify the evolutionary origins of complex cognitive abilities, including in humans. This research often assumes that great ape cognition consists of cognitive abilities (traits) that account for stable differences between individuals, which change and develop in response to experience. Here, we test the validity of these assumptions by assessing repeatability of cognitive performance among captive great apes (Gorilla gorilla, Pongo abelii, Pan paniscus, Pan troglodytes) in five tasks covering a range of cognitive domains. We examine whether individual characteristics (age, group, test experience) or transient situational factors (life events, testing arrangements or sociality) influence cognitive performance. Our results show that task-level performance is generally stable over time; four of the five tasks were reliable measurement tools. Performance in the tasks was best explained by stable differences in cognitive abilities (traits) between individuals. Cognitive abilities were further correlated, suggesting shared cognitive processes. Finally, when predicting cognitive performance, we found stable individual characteristics to be more important than variables capturing transient experience. Taken together, this study shows that great ape cognition is structured by stable cognitive abilities that respond to different developmental conditions.