The structures and stabilities of various osmium fluorides and oxyfluorides in high oxidation states have been studied by quantum-chemical calculations at DFT (B3LYP), MP2, CCSD, and CCSD( T) levels. The calculations indicate that the homoleptic fluorides all the way up to OsF8 may exist, even though OsF8 will be difficult to prepare. The last missing osmium oxyfluoride, OsOF6, is computed to be thermochemically stable against mononuclear gas-phase elimination reactions. The problem with the nonexistence of such highly fluorinated complexes appears thus to be mainly in difficult synthetic access under typical condensed-phase conditions. Matrix-isolation techniques might provide a means to characterize the highly fluorinated Os-VIII and Os-VII species.