The current thesis sought to extend the work of Stewart, Barnes-Holmes, Roche, and Smeets (2002) who reported that competing non-arbitrary stimulus relations disrupted equivalence-consistent responding in adult humans. Chapter 1 provides a review of research into stimulus equivalence, derived relational responding, and notes that the Colour-Test condition presented in the Stewart et al. (2002) study shared many features of tests traditionally used to measure executive function (EF). An introduction is also provided to cognitive theories of EF. The study presented in Chapter 2 provides support for Stewart et al. (2002) and reports that participants who were trained with black stimuli but tested with coloured stimuli showed lower levels of equivalence-consistent responding relative to other groups. Results also showed that while training with coloured stimuli is effective in undermining colour as a source of non-arbitrary stimulus control, exemplar training with black stimuli is shown not to be effective in undermining nonarbitrary stimulus control across stimulus sets. However, when exemplar training is combined with colour training participants produced the highest levels of equivalence-consistent responding Chapter 3 reports a study in which normally developing young children were presented with a table top match-to-sample training and testing procedure modified to make it appropriate to the abilities of this younger population. The modifications required participants to demonstrate criterion levels of equivalence with familiar stimuli and with novel stimuli coloured black prior to the introduction of a competing colour relation. All participants readily demonstrated equivalence-consistent responding with black stimuli and, critically, maintained equivalence when a competing colour relation was introduced. Chapter 4 presents two studies using a participant population of young children diagnosed with autism. Study 1 employed a reduced training and testing procedure but the participant failed to demonstrate equivalence class formation in any test condition. However, when six participants diagnosed with autism were subsequently exposed to the full training and testing procedures in Study 2, all six participants demonstrate equivalence-class formation with black stimuli. Critically, five of the six participants failed to maintain equivalence when a competing colour relation was introduced during testing, showing clear disruption from the competing colour relation. Chapter 5 presents a number of studies that sought to determine if training with coloured stimuli would remediate the disruption of equivalence observed for the five participants who completed Study 2 reported in Chapter 4. Study 1 demonstrated that colour training was effective in undermining non-arbitrary stimulus control within the same stimulus set for all participants. Subsequent studies showed that all participants maintained equivalence-consistent responding in the presence of competing colour relations across new sets of novel stimuli. Chapter 6 then describes two studies that sought to determine if undermining colour as a source of non-arbitrary stimulus control would also facilitate participants in maintaining equivalence in the presence of other sources of competing nonarbitrary stimulus control. Study 1 showed that participants successfully maintained equivalence-consistent responding when a competing shape relation was introduced and Study 2 showed that two participants also maintained equivalence when both shape and colour relations were simultaneously introduced during testing. The studies presented in Chapter 7 employed two experimentally naïve participants and demonstrated that competing shape relations disrupted equivalence class formation when introduced during testing. Subsequent studies showed that shape training was effective in undermining shape as a source of non-arbitrary stimulus control and participants maintained equivalence when a competing colour relation was subsequently introduced. Chapter 8 provides a summary of the findings in the current research programme and considers a number of methodological and conceptual issues arising from the studies, identifying possible weaknesses and questions that could be targeted in future research. The relationship between the current research and the cognitive concept of EF is also considered and clarified. Finally, it is concluded that further research into competing non-arbitrary stimulus control over derived relational responding may be important in understanding and treating deficits associated with autism.