In a two-step anodization process within sulphuric acid, aluminium tubes were anodized from inside to outside. The formed nanoporous alumina layers appear stacked since the pore diameters alternate between (15 +/- 7) nm and (30 +/- 10) nm. During the anodization process the current was measured and it was found that it oscillates. The oscillation rate (approximately 1 per hour) corresponds to the alternating rate of the pore diameter. During the alumina growth within the tubular substrate, the area of the alumina/aluminium interface increases continuously. Therefore, it can be supposed that the switching between two pore diameters allows the system to reduce the internal stress, which would otherwise continuously increase. Other or additional reasons for the alternating nanopore sizes could be fluctuations of concentration gradients in the electrolyte within the tubes or the formation of oxygen bubbles. (C) 2012 Elsevier B.V. All rights reserved.