The magnetic structure of the actinide dioxides (AnO2) remains a subject of intense research and is key to the development of high-accuracy computational models. A low-temperature experimental investigation of the magnetic ground-state is complicated by thermal energy released from the radioactive decay of the actinide nuclei. To establish the magnetic groundstate, we have employed high-accuracy computational methods to systematically probe different magnetic structures. A transverse 1k antiferromagnetic ground-state with Fmmm (No. 69) crystal symmetry has been established for UO2, whereas a ferromagnetic (111) ground-state with R3 ̅m (No. 166) has been established for NpO2. This has a profound impact on future computational investigations. Band structure calculations have been performed to analyse these results.