The geometry and the hyperfine structure of the four-membered rings azetidin-1-yl radical (C3H6N) and azetidine radical cation (C3H6NH+) have been studied. The geometries of both molecules were optimized using Moller-Plesset perturbation theory as well as density functional approaches, while the hyperfine structure was calculated using the multireference configuration interaction with perturbational correction (MRD-CI/B-K) and density functional methods. The geometry of the radical cation was found to be planar, while the neutral radical is puckered with an optimized puckering angle of 22-23 degrees. Employing a [6s3p/4s] AO basis the N-14 isotropic hyperfine coupling constants (hfcc’s) are 15.1 G in the neutral radical and 22.5 G in the radical cation, compared to the experimental values of 14.1 and 19.5 G. For the isotropic hfcc’s of the beta protons qualitative agreement between experiment and the present study was found. The influence of the molecular geometry and the theoretical treatment upon the values of the hfcc’s has been studied, and some trends in the hfcc’s of both molecules are discussed.