BACKGROUND Research suggesting that people with intellectual disabilities (ID) have difficulties in recognising emotions provides a rationale for studying alexithymia in this population. A number of studies have found a relationship between alexithymia and challenging behaviours in various populations and this study aims to discover if this is the case for people with ID. METHOD Cross-sectional data were collected from 96 participants with ID and 95 of their carers. The service user participants completed an alexithymia questionnaire for children while carers completed the checklist for challenging behaviour and the observer alexithymia scale. Correlational analyses were employed to explore relationships between the variables. RESULTS The relationship between service user and carer-rated alexithymia was very weak. The analysis did show significant associations between observer-rated alexithymia and challenging behaviour frequency, management difficulty and severity, but there was no significant relationship between challenging behaviour and alexithymia as rated by service users themselves. CONCLUSIONS This study suggests that observer-rated alexithymia is important in understanding challenging behaviour presented by people with ID. Service user-rated alexithymia had no association with challenging behaviour, in contrast to the results from similar research with other challenging populations.