[en] The application of ab initio single-configuration orbital theories to predict the existence and energies of autodetaching states or resonances in atoms and molecules is considered and numerical results given for the (ns)² resonances in H^- and He. In some cases (e.g. He) the conventional orbital theories (either Hartree-Fock or the local spin density approximation for exchange and correlation) give useful results but the important autodetaching states of negative ions are usefully described only by the new self-interaction-corrected (SIC) version of the local spin density approximation. The appearance and subsequent disappearance of a (1s)² resonance in a two-electron ion as the nuclear charge Z is reduced below 1 is discussed. The SIC calculation for this system displays an analogue to the 'bound state in the continuum' which Stillinger found for Z approximately equal to 0.9. (author)