Continuing our investigations of the electron structure of fluorides of transition and nontransition elements and uranium with the aid of the self-consistent field discrete-variation X/sub ..cap alpha../ method (SCF DVM-X/sub ..cap alpha../) on the basis of numerical Hartree-Fock (HF) functions, we have investigated the fluorides of xenon. In the attributions of the photoelectron spectra (PES) of the compounds XeF/sub n/ (n = 2, 4, 6), there remain questions demanding further investigation. Moreover, it is desirable to compare the results of DVM calculations with recently published data on the x-ray photoelectron spectra (XPES) of the xenon fluorides. As before, as the starting point we took the basis of the LCAO of the numerical HF functions of the Xe and F atoms, calculated in their /sup 1/S and /sup 2/P ground states. To increase the variational flexibility, the basis was supplemented by 3s Slater-type orbitals (STO) for the fluorine atoms and 5d STO for the Xe atom.