The electronic structures of the ions [MoOCl4](-), [MoOF5](2-), [MoOCl4(H2O)](-), and [MoOBr4(H2O)](-) have been calculated by spin-polarized density functional calculations. The results confirm and extend previous calculations on these ions. In addition, the output eigenfunctions and eigenvalues have been used to calculate g values and molybdenum hyperfine coupling constants. The results reproduce the trends in the experimental parameters well but tend to overestimate the magnitudes of both the g values and the hyperfine coupling constants. It is shown from the calculated EPR parameters that the contributions of low-energy charge transfer states and the covalencies of the ground and excited states are the major contributors to deviations Of g values from the spin-only value. Ligand-based spin-orbit coupling becomes important with increasing atomic number for the halides but never dominates. The molybdenum hyperfine couplings are dominated by Fermi contact terms which, in turn, originate primarily from spin polarization of the core 4s electrons. A comparison of [MoOCl4](-) with [MoOCl4(H2O)](-) indicates that the changes in EPR parameters observed on adding a sixth ligand to the coordination sphere arise from electronic structural changes due to geometrical distortions and not to specific electronic contributions from the added ligand.