The binding energy of oxygen and fluorine on the InSb(111) surface is investigated as a function of the termination of the latter using the projector augmented-wave method. It is shown that fluorine adsorption on the In-terminated surface leads, depending on the fluorine concentration, to the complete or partial elimination of the surface states induced by oxygen adsorption from the forbidden gap. The penetration of both adsorbates into the subsurface layers leads to the breaking of In–Sb bonds and the formation of chemical bonds of fluorine and oxygen with surface substrate atoms, which is the initial stage of the formation of a fluorine-containing anodic oxide layer. On the Sb-terminated InSb(111) surface, oxygen adsorption facilitates a decrease in the surface-state density in the forbidden gap. General trends in the variation in the electronic structure of the (111) surface upon fluorine and oxygen coadsorption in III–V semiconductors are discussed.