Local and electronic structures of Ni and Mn atoms in the ${\mathrm{LaNi}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{O}}_{3+\ensuremath{\delta}}$ series were studied by means of x-ray-absorption spectroscopy. The Ni and Mn K edges and Mn ${L}_{3}{/L}_{2}$ edges were analyzed. The local structure, determined by extended x-ray-absorption fine-structure spectroscopy, shows a distorted ${\mathrm{MnO}}_{6}$ octahedron in ${\mathrm{LaMnO}}_{3}.$ This distortion decreases when Ni replaces Mn in the unit cell. In samples with the same Mn/Ni ratio, the octahedron distortion is smaller in oxidized samples. This result shows that the holes induced by oxidation belong mainly to the Mn sublattice. In the ${\mathrm{LaNi}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{O}}_{3+\ensuremath{\delta}}$ series, a contraction of the ${\mathrm{MnO}}_{6}$ octahedron is coupled to an expansion of the ${\mathrm{NiO}}_{6}$ octahedron. This result is well correlated with the changes in the oxidation states deduced from x-ray-absorption near-edge spectroscopy (XANES). The Mn valence state continuously changes from the formal 3+ state in ${\mathrm{LaMnO}}_{3}$ to nearly a 4+ state in ${\mathrm{LaNi}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_{3}.$ The Ni valence state instead shifts from ${\mathrm{Ni}}^{3+}$ in ${\mathrm{LaNiO}}_{3}$ to ${\mathrm{Ni}}^{2+}$ in ${\mathrm{LaNi}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_{3}.$ Therefore, ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ are present in ${\mathrm{LaNi}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{O}}_{3+\ensuremath{\delta}}.$ Moreover, the detailed analysis of the XANES spectra points to an important mixing between the $3d$ orbitals of both cations and the $2p$ orbitals of oxygen atoms.