Geometry-optimization studies have been carried out on the neutral and singly and doubly ionized states of the first- and second-row hydrides, AHm+n(A = nitrogen, oxygen, phosphorus, sulphur; m= 0, 1, 2; n= 1, 2, 3; except H3O and H3S) and AHm+4(A = nitrogen, phosphorus; m= 0, 1, 2). Calculations have been performed at both the SCF and CASSCF levels. Comparison with experimental geometries show that for the first-row hydrides, the underestimation of the bond lengths and overestimation of the bond angles found at the SCF level are successfully corrected at this MCSCF level. For the second-row hydrides the errors in the SCF values are smaller, whilst the subsequent MCSCF corrections are close to those for the first-row hydrides, yielding poorer agreement with experimental geometries. Barriers to deprotonation of the dications have been calculated to interpret mass-spectrometric charge-stripping data. All the dications studied, except OH2+, NH2+, H2O2+ and NH2+4, have relatively large barriers, in qualitative agreement with experiment. The calculated adiabatic ionization energies for the monocations of nitrogen and oxygen are, except for NH+4, significantly larger than the experimental values. This discrepancy is unlikely to reflect inadequancies in the calculations and points to excited vibrational states of the monocations being involved experimentally.