A survey is presented of the lower excited states of the tetrahedral oxy-anions having a d0transition metal at the centre, with particular emphasis on the triplet states. The principal question addressed concerns the spin-orbit coupling mechanism in these ions. It appears that the symmetry of the molecular orbitals involved in the first excitation is such that—at least for the 3d compounds VO3-4, CrO2-4, MnO−4—the major spin-orbit coupling should occur on the oxygen ligands. Two quantitative problems are considered: the radiative lifetime of the3Ttstate, and the zero-field splitting of this multiplet if spin-orbit coupling is the dominant interaction determining the splitting. The results of the theoretical analysis are compared with recent information on the luminescent triplet states of K2Cr2O7, YVO4and CaMoO4obtained by E.P.R. The radiative lifetime of 4 ms calculated for VO3=4is in excellent agreement with the scarce experimental information. The spin orbit coupling, however, does not appear to be the dominant interaction determining the multiplet splitting of the 3d and 4d compounds. The tetrahedral ions, in accordance with the Jahn-Teller effect, suffer a distortion on excitation and a single orbital state lies lowest with a fine structure characteristic for a situation of low symmetry.