We report a comprehensive study of the crystal structure of (Ga1-xZnx)(Ni1-xOx) solid solution nanopartides by means of neutron and synchrotron X-ray scattering. In our study, we used four different types of (Ga1-xZnx)(Ni1-xOx) nanopartides, with diameters of 10-27 nm and x = 0.075-0.51, which show energy band gaps from 2.21 to 2.61 eV. Rietveld analysis of the neutron diffraction data revealed that the average crystal structure is hexagonal wurtzite (space group P6(3)mc) for the larger nanopartides, while the crystal structure of smaller nanoparticles is disordered hexagonal. Pair-distribution-function analysis found that the intermediate crystal structure retains a "motif" of the average one; however, the local structure is more disordered. The implications of disorder on the reduced energy band gap are discussed.