Reliable theoretical data on spectroscopy and spin-orbit matrix elements are computed for the lowest electronic states of SH+ and LiS+ ions. Accurate spectroscopic predictions for their excited electronic states are given. For SH+, polarization minima at large internuclear distances are located in addition to the strongly bound electronic states already known. For LiS+, our calculations confirm that the electronic ground state of this ion is of (3)Sigma(-) species and reveal the existence of a (1)Delta state presenting a potential well as deep as the potential of the ground state. Moreover, the LiS+ electronic excited states potential energy curves possess shallow potential minima in the molecular region and at long-internuclear distances. Generally, these shallow minima may be populated during low energy collisions between the corresponding atomic fragments. Finally, spin-orbit calculations have allowed giving accurate determinations of the spin-orbit splittings for these cations and elucidation of the predissociation mechanisms of SH+ leading to the formation of the S+ and H species in their electronic ground states. Accordingly, long-lived SH+ ions can be found in the (XE-)-E-3, a(1)Delta and b(1)Sigma(+) electronic states and the rovibrational levels of LiS+ in its electronically excited and ground states should be weakly perturbed. (C) 2006 Elsevier Inc. All rights reserved.