Using the cups task, in which subjects are presented with limited visual or auditory information that can be used to deduce the location of a hidden reward, Call (2004) found prima facie evidence of inferential reasoning by exclusion in several great ape species. One bonobo (Pan paniscus) and two gorillas (Gorilla gorilla) appeared to make such inferences in both the visual and auditory domains. However, common chimpanzees (Pan troglodytes) were successful only in the visual domain, and Bornean orang-utans (Pongo pygmaeus) in neither. The present research built on this paradigm, and Experiment 1 yielded prima facie evidence of inference by exclusion in both domains for two common chimpanzees, and in the visual domain for two Sumatran orangutans (Pongo abelii). Experiments 2 and 3 demonstrated that two specific associative learning explanations could not readily account for these results. Because an important focus of the program of research was to assess the cognitive capacities of lesser apes (family Hylobatidae), we modified Call’s original procedures to better suit their attentional and dispositional characteristics. In Experiment 1, testing was also attempted with three gibbon genera (Symphalangus, Nomascus, Hylobates), but none of the subjects completed the standard task. Further testing of three siamangs (Symphalangus syndactylus) and a spider monkey (Ateles geoffroyi) using a faster method yielded prima facie evidence of inferential reasoning by exclusion in the visual domain among the siamangs (Experiment 4).