The spectroscopic constants of the excited doublet and quartet states of AlS have been calculated from potential energy functions obtained by the internally contracted multireference configuration interaction (MRCI) approach. Most of these states have not yet been observed. The shape of the electric dipole and transition moment functions are discussed. The spin-orbit constants and the spin-orbit couplings between different states have been evaluated for those cases in which such couplings are responsible for the perturbations of the spectra. The results are compared with similar data for the isoelectronic AlO. For the low lying electronic states of the AlS cation, the potential energy functions and the spectroscopic constants are reported. The electronic ground state of AlS- was found to be the only bound state.