Eight chimpanzees (Pan troglodytes), five bonobos (Pan paniscus), five gorillas (Gorilla gorilla), and seven orangutans (Pongo pygmaeus) were presented with two invisible object displacement tasks. In full view of the subject, a food item was hidden under one of three opaque cups resting on a platform and, after an experimental manipulation, the subject was allowed to select one of the cups. In the rotation task, the platform was rotated 180° while the subject remained stationary. In the translocation task, the platform remained stationary while the subject walked to the opposite side from where she saw the reward being hidden. The final position of the food relative to the subject was equivalent in both tasks. Single displacement trials consisted of only one manipulation, either a rotation or a translocation, whereas double displacement trials consisted of both a rotation and a translocation. We also included no displacement trials in which no displacements took place. No displacement trials were easier than single displacements which, in turn, were easier than double displacements. Unlike earlier studies with children, there was no difference in performance between rotation and translocation displacements. Overall, apes performed above chance in all conditions, but chimpanzees outperformed the other species. This study reinforces the notion that the great apes use an allocentric spatial coding. Am. J. Primatol. 72:349–359, 2010. © 2010 Wiley-Liss, Inc.