Nanocrystalline Ni-doped gadolinium oxide (Gd 1.90 Ni 0.10 O 3Àd , GNO) is synthesized by co-precipitation method. The as-prepared sample is annealed in vacuum at 700°C for 6 h. Analyses of the x-ray diffractogram by Rietveld refinement method, transmission electron microscopy and Raman spectroscopy of GNO recorded at room temperature confirmed the pure crystallographic phase and complete substitution of Ni-ions in Gd 2 O 3 lattice. Magnetization (M) as a function of temperature (T) and magnetic field (H) is measured by a superconducting quantum interference device magnetometer, which suggests the presence of ferromagnetic/antiferromagnetic phases together with a paramagnetic phase. From the M-T curve it can be shown that the ferromagnetic phase dominates over para-/antiferromagnetic phases in the temperature range of 300-100 K, but from 100 K to 50 K, the antiferromagnetic phase dominates over ferro-/paramagnetic phases. Hysteresis loops recorded at different temperatures indicate the presence of weak ferro-/antiferromagnetism, which dominates in the low field region ($ 4000 Oe), above which magnetization increases linearly. The sharp increase of magnetization in M-T curve observed in the temperature range of 50-5 K confirms the presence of dominating ferromagnetic plus paramagnetic phase over antiferromagnetic part. For the first time a combined formula generated from threedimensional (3D) spin wave model and Johnston formula is proposed to analyze the coexistence of different magnetic phases in different temperature ranges. Interestingly, the combined formula successfully explains the co-existence of different magnetic phases along with their contribution at different temperatures. The onset of ferromagnetism in Gd 1.90 Ni 0.10 O 3Àd is explained by oxygen vacancy mediated F-centre exchange (FCE) coupling mechanism.