The structure of the fluorite-related zirconium oxynitride Zr2ON2 has been refined against a combination of laboratory X-ray and time of flight neutron powder diffraction data. The structure is of the bixbyite (C-M2O3) type. The high symmetry of the powder diffraction pattern does not allow us to easily distinguish between fully ordered, fully disordered, or partially ordered anion models. However, Rietveld refinements against both high and medium resolution neutron powder diffraction data clearly favour a statistical distribution of oxide and nitride anions over a single crystallographic site which is contrary to the predictions of previous calculations. The space group is Ia3̄ (No. 206), with a = 10.13940(7) Åat 298 K and Z = 16. This symmetry and unit cell are retained at low temperatures (a = 10.1250(1) Å at 4.5 K). Partial oxidation reveals the existence of a phase with N2 molecules weakly bound and the stoichiometry ZrO2(N2)0.028(1). We also report the isostructural hafnium oxynitride Hf2ON2 (Ia3̄ with a= 10.0692(2) Å at 298 K as determined using laboratory X-ray diffraction data). © 1999 Academic Press.