Line lists for sulphur containing molecules SH (the mercapto radical) and NS are computed as part of the ExoMol project. These line lists consider transitions within the ground electronic state for isotopologues of SH and NS. Ab initio potential energy (PEC), and spin-orbit coupling (SOC) curves are computed and then improved by fitting to experimentally observed transitions. Fully ab initio dipole moment curves (DMCs) computed at the high level of theory are used to produce the final line list. For SH, our fit gives a root-mean-square (rms) error of 0.03cm^-1^ between the observed (v_max_=4, J_max_=34.5) and calculated transitions wavenumbers; this is extrapolated such that all possible X bound states are considered. For ^32^SH the resulting line list contains about 81,000 transitions and 2300 rovibronic states, considering levels up to vmax=14 and Jmax=60.5. For NS the refinement using a combination of experimentally-determined frequencies and derived energy levels rms errors of 0.002cm^-1^ and 0.03cm^-1^, respectively. Each NS calculated line lists includes around 3.2 million transitions and 31000 rovibronic states with a vibrational range up to v=53 and rotational range to J=235.5 which covers up to 39000cm^-1^. Both line lists should be complete for temperatures up to 5000K. Example spectra simulated using this line list are shown and comparisons made to the existing data in the CDMS database.