Aluminum materials and aluminized parts are oxidatively anodized at a bath temperature of 0.degree. to 15.degree. C. and preferably, 0.degree. to 10.degree. C. to produce an anodized layer of aluminum oxide more than 4 microns thick, which is hard, abrasion-proof and can be stained. The anodizing is bath used while conducting air free of or low in carbon dioxide through the bath. It is free of substances which limit the oxide layer to maximally a thickness of about 1 micron (forming layer) and contains 10 to 500 g trisodium phosphate or tripotassium phosphate per liter. In partially aluminized parts, no destruction of the base material occurs during the aluminizing.