Under strongly reducing conditions at high temperatures titania develops a specific surface morphology, comprising a regular array of fibers with a diameter in the sub-micrometer range. By a chemical diffusion experiment in a defined oxygen potential gradient it is shown that this surface structuring is caused by a diffusion-driven morphological instability of an advancing reaction front (surface). The kinetics of the process is analyzed in terms of linear transport equations. The conditions for the occurrence of the surface instability are discussed and the required materials properties are analyzed. The observed surface structuring is not restricted to titania, rather it has to occur in all nonstoichiometric compounds with predominant cation mobility.