Abstract: This invention refers to a procedure for anodising aluminium or aluminium alloys in which an aluminium or an aluminium alloy part is submerged an in an aqueous solution at a temperature between 0° C. and 140° C., preferably between 0° C. and 130° C., in which said solution includes: sulphuric acid, tartaric acid, and at least one inorganic salt of an element selected between at least one transition metal, a lanthanide element, an actinide, and combinations of them, and applying a controlled potential difference, obtaining layers of aluminium oxide with properties as good as or even better than those obtained through anodising in traditional chromic acid solutions.