Nanoparticles of ZrO2 and HfO2 with sizes around 5 nm are – depending on the production route - found in the cubic or tetragonal or monoclinc phase. To shed some light into this difference, an analysis of crystal structure, distances, and symmetry around the cations was performed on alumina coated nanoparticles prepared by the microwave plasma process. Within the range of accuracy, electron-diffraction and -microscopy revealed a possibly cubic cation lattice for both materials. In the case of ZrO2, the evaluation of the amplitude of the modified radial distribution function derived from extended x-ray absorption fine structure (EXAFS) data lead to a structure with a narrow distribution of oxygen ions in the first shell of neighbors. This is expected for the cubic structure. Comparing the imaginary part with model calculations, a distinct similarity with the cubic structure is obvious. In the second shell of neighbors, consisting of metal ions, one radial distribution peak is expected and found experimentally. Perturbed angular correlation measurements indicate a pronounced disorder of the positions of the first neighbors of the metal ions. Together with the EXAFS observation of a narrow radial distribution of the first neighbor oxygen ions, these measurements provide evidence for a randomc distribution of Zr-O bond angles in the vicinity of their crystallographic positions. Above 500°C a partially reversible transformation to almost perfect tetragonal symmetry is observed. Therefore, one has to conclude that the cubic structure with disordered anion lattice is more stable than the tetragonal one at room temperature. Structural relationships like this are unknown in coarse-grained material.