Children with an intellectual disability (ID) and/or autism spectrum disorder (ASD) are known to suffer from significantly more sleep problems, anxiety and challenging behaviour (CB) than typically developing children (TD), yet little is known about the relationship between these factors in the child ID/ASD population. The study aim was to examine these relationships. We hypothesised that there would be significant positive correlations between the three factors and that sleep problems and anxiety would predict a significant amount of the variance in levels of CB. Parental measures of sleep problems, anxiety and CB were completed by 187 parents of children with ID and/or ASD. Significant positive associations were found between the three factors. A hierarchical multiple regression showed that medication, sleep problems and anxiety accounted for 42% of the variance in CB, with a large effect size. These findings suggest that these relationships should be considered during clinical practice, particularly in the case of CB interventions where sleep problems and/or anxiety are also present. (Contains 4 tables.)