There exists a low-frequency relaxation internal friction peak in La2NiO4+δwithδ=0.071, 0.110, 0.135 and 0.140, the peak position shifting to higher temperatu re, when more excess oxygen is incorporated. At δ=0.087 two peaks were obse rved which may be attributed to the jump of the interstitial oxygen atoms in the diff erent kind of the one-dimensional ordering phase formed by phase separation. At δ=0.038 two peaks were also observed which may be attributed to the jump of the i nterstitial oxygen atoms in the low-temperature tetragonal phase and the one-dimensional ordering phase formed by phase separation.