Background: Cognitive skills thought to be necessary to undertake cognitive-behavioural therapy (CBT) include the ability to recognize emotions, link events and emotions, and recognize cognitive mediation. These skills have been assessed in people with intellectual disabilities, but not in those who also have psychosis. Materials and methods: Tasks assessing receptive language ability and cognitive skills including the ability to differentiate between behaviours, thoughts and feelings were administered to 50 participants who had intellectual disabilities and psychosis. Results: The majority of participants were able to link events and emotions and differentiate behaviours and feelings. Participants found any task involving cognitions significantly more difficult. Performance on recognizing emotions, linking events and emotions and on some of the cognitive mediation and differentiation tasks was associated with receptive language ability. Conclusions: People with intellectual disabilities and psychosis have some of the skills thought to be required to undertake cognitive behaviour therapy. Recognizing cognitions and cognitive mediation is particularly challenging. The differentiation task introduced in this study may usefully supplement existing assessments.