We used multiple conditional discriminations to study the inferential abilities of pigeons. Using a five-term stimulus series, pigeons were trained to respond differentially to four overlapping pairs of concurrently presented stimuli: A+ B-, B+ C-, C+ D-, and D+ E-, where plus and minus indicate the stimulus associated with reinforcement and extinction, respectively. Transitive inference in such situations has been defined as a preference for Stimulus B over Stimulus D in a transfer test. We measured this and other untrained preferences (A vs. C, A vs. D, B vs. E, etc.) during nonreinforced test trials. In three experiments using a novel, rapid training procedure (termed autorun), we attempted to identify the necessary and sufficient conditions for transitive inference. We used two versions of autorun: response-based, in which the subject was repeatedly presented with the least well-discriminated stimulus pair; and time-based, in which the subject was repeatedly presented with the least-experienced stimulus pair. In Experiment 1, using response-based autorun, we showed that subjects learned the four stimulus pairs faster than, but at a level comparable to, a previous study on transitive inference in pigeons (Fersen, Wynne, Delius, & Staddon, 1991), but our animals failed to show transitive inference. Experiments 2 and 3 compared time- and response-based autorun. Discrimination performance was maintained, but transitive inference was observed only on the second exposure to the response-based procedure. These results show that inferential behavior in pigeons is not a reliable concomitant of good performance on a series of overlapping discriminations. The necessary and sufficient conditions for transitive inference in pigeons remain to be fully defined.