In many cases, alumina scales are assumed to grow predominantly by oxygen diffusion, but some authors have found that the growth can be controlled by aluminium diffusion. These mechanisms can be modified by active elements. The problem with alumina is that there is a lack of data about self-diffusion coefficients, and, due to the stoichiometry of alumina, diffusion data correspond to an extrinsic diffusion mechanism so that it is not possible to compare oxygen and aluminium diffusion coefficients. In order to obtain information about the alumina scale growth mechanism, oxygen (O-18) and aluminium (Al-26) self-diffusion coefficients in Al2O3 were determined in the same materials and in the same experimental conditions, thus allowing a direct comparison. For both isotopes, bulk and sub-boundary diffusion coefficients were determined in single crystals of undoped alumina. Grain-boundary diffusion coefficients have been computed only for oxygen diffusion in polycrystals. Oxygen diffusion has been also studied for yttria-doped alpha-alumina in the lattice, sub-boundaries and grain boundaries. Oxygen and aluminium bulk diffusion coefficients are of the same order of magnitude. In the sub-boundaries, aluminium diffusion is slightly faster than oxygen diffusion. Yttria doping induces a slight increase of the oxygen bulk diffusion, but decreases the grain-boundary diffusion coefficients on account of segregation phenomena. These results are compared with the oxidation constants of alumina former alloys (alloys which develop an alumina scale by oxidation). It appears that neither lattice self-diffusion nor grain boundary self-diffusion can explain the growth rate of alumina scales. Such a situation is compared to the case of Cr2O3.