We report parameter-free self-consistent pseudopotential Green's-functions of the electronic structure of self-interstitials in Si at tetrahedral sites and of P and C interstitials in GaP, also at the tetrahedral sites. We find that the number, relative energy positions, and wavefunction character of the localized states of deep interstitials are strikingly similar to those of deep substitutional donor impurities and explain this result in terms of simple physical considerations. In the case of the Si self-interstitial, our results are significantly different from earlier results of Extended-Hückel calculations. We find no deep states in the energy gap, which provides a natural explanation of the fact that self-interstitials at tetrahedral sites have not been detected by either EPR or DLTS. Our results have also motivated a reinterpretation of experimental data on the migration of self-interstitials. © 1983.