Described herein is a method for treatment of at least one surface of a substrate at least partially made of aluminum and/or an aluminum alloy, including at least a step of contacting said surface with an acidic aqueous composition (A) including one or more metal compounds (M) selected from the group of titanium compounds, zirconium compounds, and hafnium compounds and one or more linear polymers (P) containing (m1) N,N-dimethyl (meth)acryl amide, (m2) vinylphosphonic acid, and (m3) (meth)acrylic acid in form of their polymerized monomeric units, the one or more linear polymers (P) being included in the acidic aqueous composition (A) in an amount of 50 to 5000 ppm. Also described herein is an acidic aqueous composition (A), a master batch to produce the acidic aqueous composition (A), a method of using the acidic aqueous composition (A) for treating surfaces, and substrates comprising the treated surfaces.