The explanation of the emergence of untaught behaviour has been a topic of considerable interest in behaviour analysis. The experiments in this thesis were designed to examine some of the processes underlying these emergent relations. In doing this, two different paradigms were examined - stimulus equivalence and transitive inference. The experiments leading to a formal definition of equivalence relations are reported, and the demonstration of cognitive abilities with both humans and non-humans described. The explanations proposed for the basis of stimulus equivalence are discussed. Data from five experiments are then presented. Experiment 1 considered the role of naming in stimulus equivalence and Experiment 2 contrasted this performance with the establishment of transitive inference, both experiments being carried out with adults with learning disabilities as subjects. The results from these experiments suggested that while naming behaviour may help to establish emergent relations, it may not be the basis of stimulus equivalence, and that it may be possible to account for performance on both stimulus equivalence and transitive inference tests in terms of reinforcement contingencies. While subjects who display stimulus equivalence are likely to also display transitive inferences, the reverse relation may not be true. Experiments 3 and 4 examined the effects of a disruption of the baseline relations on performance on transitive inference and stimulus equivalence tasks. These experiments were both carried out with normally able adults, adults with learning disabilities, and normally developing young children. Experiment 5 was a replication of Experiment 4 with a tighter methodology and a larger number of subjects with learning disabilities. It is suggested that the results obtained in Experiments 4 and 5 can be explained by the development of contextual control of the equivalence relations. The results from these experiments suggested that the transitive inference and stimulus equivalence paradigms may respectively be concrete and abstract examples of more general emergent relations. These paradigms may also prove to be very useful teaching tools for helping to establish emergent relations.