The heavier alkali-metal monosulfides ͑KS, RbS, CsS, and FrS͒ have been studied by high-level ab initio calculations. The RCCSD͑T͒ method has been employed, combined with large flexible valence basis sets. All-electron basis sets are used for potassium and sulfur, with effective core potentials being used for the other metals, describing the core electrons. Potential-energy curves are calculated for the lowest two neutral and cationic states: all neutral monosulfide species have a 2 ⌸ ground state, in contrast with the alkali-metal monoxide species, which undergo a change in the electronic ground state from 2 ⌸ to 2 ⌺ + as the group is descended. In the cases of KS, RbS, and CsS, spin-orbit curves are also calculated. We also calculate potential-energy curves for the lowest 3 ⌺ − and 3 ⌸ states of the cations. From the potential-energy curves, spectroscopic constants are derived, and for KS the spectroscopic results are compared to experimental spectroscopic values. Ionization energies, dissociation energies, and heats of formation are also calculated; for KS, we explore the effects of relativity and basis set extrapolation on these values.