Relativistic corrections beyond the simple one-electron mass-velocity-Darwin (MVDI) approximation to the ground-state electronic energy of H2S are determined at over 250 geometries. The corrections considered include the two-electron Darwin, the Gaunt and Breit corrections, and the one-electron Lamb shift. Fitted correction surfaces are constructed and used with an accurate ab initio nonrelativistic Born-Oppenheimer potential, determined previously (J. Chem. Phys. 115 (2001) 1229), to calculate vibrational and rotational levels for (H2S)-S-32. The calculations suggest that one- and two-electron relativistic corrections have a noticable influence on the levels of H2S. As for water, the effects considered have markedly different characteristics for the stretching and bending states. (C) 2002 Elsevier Science B.V. All rights reserved.