Ab initio (UHF, UMP2) and density functional calculations, basis sets from 6-31G to TZP, have been performed on a series of simple aminoxyls, either acyclic (Me(2)NO, (CF3)(2)NO) or cyclic (from aziridine-N-oxyl to piperidine-N-oxyl) in order to assess their equilibrium geometry and the features of the nitrogen inversion. The results were in good agreement with the few available experimental results. The main problem that arises from the aminoxyl group is its variable geometry, even in apparently structurally close situations, e.g. planar in pyrrolidine-N-oxyl and pyramidal in piperidine-N-oxyl. In an attempt to offer a rationalization of these unexplained differences, we applied to dimethylaminoxyl geometrical constraints concerning successively the C-N bond length, the C-N-C bond angle, and the H-C-N-C torsion angles Phi and Psi on both sides of the aminoxyl group. Modifying the C-N bond length showed no effect on the out-of-plane deformation of the group. On the contrary, increasing the C-N-C : angle diminished the out-of-plane deformation, thus explaiming the planarity of the di(tert-butyl)aminoxyl. Unexpectedly,the values of the torsion angles Phi and Psi exerted an important influence upon the planarity-pyramidality preference; and the values imposed by the ring geometry in pyrrolidine-N-oxyl and piperidine-N-oxyl corresponded respectively to planar and pyramidal structures, as experimentally found.