The process for manufacturing support materials for offset-printing plates is carried out in two stages. These materials are in the form of plates, foils, or strips, composed of aluminum, or an alloy thereof, which have been roughened by chemical, mechanical and/or electrochemical treatment. These two stages comprise an anodic oxidation in (a) an aqueous electrolyte based on sulfuric acid, and in (b) an aqueous electrolyte which is different from that in stage (a). An electrolyte with a content of dissolved oxoanions of boron, vanadium, molybdenum, tungsten, and/or carbon is employed in stage (b), and the treatment is carried out at a voltage between about 10 and 100 V, at a temperature of from about 10.degree. to 60.degree. C., and for a duration of from about 1 to 60 seconds. The electrolyte is an acid or, in particular, a salt with the above-mentioned anions. Following stage (b), it is also possible to carry out an additional treatment to impart hydrophilic properties to the support material.