We report theoretical results for the bonding of NO to the threefold (fee) position of the Cu(lll) surface. Both, N- and O-down orientations have been considered. Our study is based on several cluster models and nb initio wave functions. We found that the NO/Cu(lll) interaction is dominantly ionic in nature, with a small but noticeable rr covalent contribution for the N-down orientation only. The ionic nature of the bond has important consequences as an avoided crossing between two electronic states of ionic and neutral character. The existence of this avoided crossing interaction indicates that the adsorption process is nonadiabatic. Finally, the analysis of the vibrational frequencies of adsorbed NO predicts that a O-down species may exist in the NO/Cu(111) system. This is the first time that an O-down species is proposed in Cu surfaces.