The absolute cross sections for the production of X2+ and X3+ ions following absorption of monochromatised SOLEIL synchrotron radiation by the HX+ hydride molecular ions (X = S, Cl) are presented as a function of photon energy in the region of the X2p ionisation thresholds (B180 eV and B220 eV for sulphur and chlorine, respectively). The experimental results are interpreted with the help of extensive ab initio density functional theory (DFT) and post-Hartree–Fock configuration interaction calculations including spin–orbit coupling to compute the absorption oscillator strengths of the X 2p core excitations to valence and Rydberg states. In order to account for all the experimental features, the calculations must include vibrational dynamics and spin–orbit coupling. Similar experimental data are also presented for the sulfaniumyl H2S+ molecular ion.