The Ni and the Nd environments in the stoichiometric and oxidized Nd2NiO4+delta samples have been investigated using EXAFS spectroscopy. In the stoichiometric compound, the Ni and Nd oxygen coordination numbers have been found to be in good agreement with the neutron diffraction crystallographic data. For the oxidized sample, a rearrangement compatible with an increment of the number of oxygen atoms around the Nd ions is found. This Increment is consistent with the location of the excess oxygen atoms between the consecutive neodymium (rare earth) layers. While the Raman spectra of the stoichiometric sample is in accordance with the group theory predictions for a Cmca symmetry, oxidized sample spectra are clearly dominated by the perturbations introduced in the crystal by the oxygen defects.