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 OsVIII and OsVII species.