The invention is in a composition and process for the chromium free passivating postrinsing of conversion layers on metals before the application of a paint or adhesive. The conversion layers can be on the bases of phosphate layers, at least two polyvalent metal ions with complex formers, titanium, zirconium and/or hafnium. The postrinsing agent is an aqueous solution which has been adjusted to a pH value of up to 5 and which contains an aluminum fluorozirconate having an Al:Zr:F mole ratio of (0.15 to 8.0):1:(5 to 52), and in which solutions the total concentration of Al+Zr+F is 0.1 to 8.0 g/l. The postrinsing solutions may additionally contain at least one of the anions benzoate, caprylate, ethyl hexoate, salicylate in a total concentration of 0.05 to 0.5 g/1 and may preferably be adjusted to the required pH value with cations of volatile bases, such as ammonium, ethanolammonium and di- and triethanolammonium. The paint is subsequently applied suitably by cathodic electrocoating or powder coating or from a low-solvent high-solids paint.The rinsing treatment is over a period of 1 to 120 seconds at temperatures of 20.degree. to 80.degree. C. The invention is used as a pretreatment to the application of a paint coating, film coating or adhesive coating.