The present invention relates to the field of phosphating for corrosion-protective pretreatment of zinc surfaces, being directed toward the use of largely nickel- and cobalt-free zinc phosphating solutions. The present invention makes available an alternative to trication zinc phosphating, in which the zinc surfaces of a component are firstly, before zinc phosphating, passivated with an alkaline composition containing iron(III) ions, and thereby preconditioned for a largely nickel- and cobalt-free zinc phosphating operation. In a further aspect, the invention relates to a component, in particular an automobile body, that comprises at least in part surfaces made of zinc, the zinc surfaces being covered by a two-layer system made up of a first, inner passive layer containing iron and resting on the zinc surface, and a second, outer crystalline zinc phosphate layer resting on the inner layer.