The absolute cross sections for the production of X2+ andX3+ 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 (∼180 eV and∼220 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.