The structures and relative stabilities of the cationic forms of the halogen dioxides have been studied by means of ab initio molecular orbital calculations. For fluorine and chlorine-containing compounds the geometries and the harmonic vibrational frequencies of all possible isomers were calculated at the QCISD/6-311+G(2d) level of theory. For bromine and iodine-containing compounds the effective core-potential basis sets of Hay and Wadt, modified to include a set of diffuse functions and two sets of polarization functions, were employed. For all systems the final energies were obtained at the QCISD(T)/6-311+G(3df) level of theory. In addition, multiconfiguration-based methods (CASSCF and CASPT2) have also been used. The relative stabilities of structures XOO+ and OXO+ are greatly reduced relative to those observed for the corresponding neutral species. In fact, for Cl and I derivatives, the lowest energy isomer corresponds to the symmetric OXO+ open-chain species. The corresponding cyclic structures arise as local minima on the respective potential energy surfaces, but they lie much higher in energy than the OXO+ open-chain form or the XOO+ isomer. There are significant differences in bonding between XOO+ and OXO+, the X-O interaction in OXO+ being more covalent than in XOO+. There are also trends along the series that reflect the pronounced disparity between the electron affinity of F+ and those of the heavier atoms of the group. FOO+ species can be viewed as F(P-2)-O-2(+) complexes, whereas XOO+(X = Br, I) species can be regarded as X+(P-3)-O-2 complexes. The OXO+ open-chain species have an electron charge distribution similar to that of the ozone molecule, reflecting the same number of valence electrons in each case.