We report a theoretical investigation of the (X) over tilde (2)A '' and (A) over tilde (2)A ' electronic states of HSO/HOS. Three-dimensional potential energy surfaces for the (X) over tilde (2)A '' and (A) over tilde (2)A ' electronic states of HSO/HOS have been calculated ab initio by the core-valence MR-SDCI+Q/[aug-cc-pCVQZ(S,O),aug-cc-pVQZ(H)] method, and near-global potential energy surfaces have been constructed. These surfaces have been used, in conjunction with our computer program DR, for calculating HSO/HOS rovibronic energies in the electronic states (X) over tilde (2)A '' and (A) over tilde (2)A '. Both electronic states have nonlinear equilibrium geometries and they correlate with (2)Pi states at the H-S-O and H-O-S linear configurations so that they exhibit the double Renner effect. The present DR calculation of the rovibronic energies for the (X) over tilde (2)A '' and (A) over tilde (2)A ' electronic states of HSO/HOS is complicated by the Renner-interaction breakdown of the Born-Oppenheimer approximation and by HSO/HOS isomerization. Calculated energies are reported together with analyses of the rovibronic wave functions for selected states. These analyses explore the interplay between the effects of, on one hand, Renner interaction and, on the other hand, isomerization tunneling in the rovibronic dynamics of HSO/HOS.