A computational study is presented of the structural, electronic, and magnetic properties of ${\mathrm{U}}_{3}$O${}_{8}$ and Np${}_{2}$O${}_{5}$, which are actinide oxides in a higher oxidation state than the tetravalent state of the common dioxide phases, UO${}_{2}$ and NpO${}_{2}$. The calculations are based on the density functional theory+$U$ approach, in which additional Coulomb correlations on the actinide atom are taken into account. The calculated properties of these two higher oxidized actinide oxides are analyzed and compared to those of their tetravalent analogs. The optimized structural parameters of these noncubic oxides are found to be in reasonable agreement with available experimental data. ${\mathrm{U}}_{3}$O${}_{8}$ is predicted to be a magnetic insulator, having one U atom in a hexavalent oxidation state and two U atoms in a pentavalent oxidation state. For Np${}_{2}$O${}_{5}$, which is also predicted to be an insulator, a complicated noncollinear magnetic structure is computed, leading to a nonzero overall magnetization with a slight antiferromagnetic canting. The calculated electronic structures are presented and the variation of the U $5f$ or Np $5f$--O $2p$ hybridization with the oxidation state is analyzed. With increasing oxygen content, the nearly localized 5$f$ electrons of the actinide elements are more positioned near the Fermi level and the hybridization between 5$f$ and 2$p$ states is markedly increased.