The problem of inorganic dust formation is discussed for the conditions of cool late-type giants and supergiants having an oxygen rich element composition. Particular emphasis is put on the formation of the primary condensates, i.e., the first kind of grains forming from the gas phase. By explorative chemical equilibrium discussion it has been shown that titanium oxides, especially TiO₂ molecules, are the most probable candidates to nucleate first. Though SiO is by far the most abundant reacting oxygen bearing species it can usually be ruled out at high temperatures, because effective condensation takes place only below 600 K under typical M star conditions. The situation regarding the nucleation of aluminium bearing molecules to form corundum is not as clear. Though corundum has an extremely high stability the constituting aluminium oxides are much less stable at temperatures above the onset of TiO₂ condensation. Therefore, it might be argued that corundum is also not likely to constitute the first condensate in the outflows of M stars.