A multicoat paint system comprising, lying atop one another in this order,(1) at least one first basecoat comprising basecoat material (A), (2) a second, color and/or effect basecoat comprising basecoat material (B), and (3) at least one transparent coating comprising clearcoat material (C). The basecoat material (A) of the first basecoat comprises at least one binder (a.1), at least one color and/or effect pigment (a.2), and a corrosion-inhibiting component (a.3) having an aromatic parent structure (GK), which has at least two unidentate, potentially anionic ligands (L1) and (L2) with electron donor function attached covalently to (GK), and/or which possesses substituents (SU) which are attached covalently on the aromatic parent structure (GK), and which have at least two covalently attached, unidentate, potentially anionic ligands (L1) and (L2) with electron donor function, the ligands (L1) and (L2) capable of complex formation after the multicoat paint system has been thermally cured.