Oxygen intercalation/deintercalation in Pr2NiO4+delta and Nd2NiO4+delta was followed by in situ neutron powder diffraction during electrochemical oxidation/reduction, in a dedicated reaction cell at room temperature. For both systems three phases, all showing the same line width, were identified. The starting phases Pr2NiO4.23 and Nd2NiO4.24, considered with an average orthorhombic Fmmm symmetry, although both show a slight monoclinic distortion, get reduced in a two-phase reaction step to tetragonal intermediate phases with 0.07 <= delta <= 0.10 and P4(2)/ncm space group, which on further reduction transform, again in a two-phase reaction step, toward the respective stoichiometric (Pr/Nd)(2)NiO4.0 phases, with Bmab space group. Electrochemical oxidation does, however, not proceed fully reversibly for both cases: while the reoxidation of Nd2NiO4+delta is limited to the tetragonal intermediate phase with delta = 0.10, the homologous Pr2NiO4+delta can be reoxidized up to delta = 0.17, showing orthorhombic symmetry. For the intermediate tetragonal phase, we were able to establish for Pr2NiO4.09 a complex anharmonic displacement behavior of the apical oxygen atoms, as analyzed by single-crystal neutron diffraction and maximum entropy analysis, in agreement with a low-T diffusion pathway for oxygen ions, activated by lattice dynamics.