The limited existing research on diabetes management and intellectual disabilities (ID) highlights the need for further exploration of the concept of responsibility. This study explored repertoires of responsibility in accounts of managing diabetes for adults with ID. Fourteen semi‐structured interviews were conducted in the UK with seven adults with mild/moderate ID and type 1 or 2 diabetes and seven people who they nominated as supporting their diabetes management. A discursive psychological analysis found that interpretative repertoires relating to competence, independence and accountability were drawn on to construct multiple and sometimes conflicting versions of responsibility. Within these repertoires people with ID were positioned in conflicting ways; as competent, personally responsible, and entitled to independence and choice, but as also lacking competence, dependent on others and incapable of overall accountability. People with ID often took up empowering positions defending against an incompetent identity. Supporters built accounts which negotiated dilemmatic repertoires on the dual responsibilities of empowering adults with ID to self‐manage and managing risk to support good and safe care. The implications of available discursive resources and the ways in which they are mobilised are considered.