The transpassive dissolution of Fe-12%Cr and Fe-25%Cr alloys in near-anhydrous phosphoric acid/acetic acid mixtures has been studied by conventional voltammetry and electrochemical impedance spectroscopy. Both steady-state and transient techniques point to two parallel pathways for the process involving oxidative dissolution of Cr as Cr(VI) and isovalent dissolution of Fe most probably mediated by an electrolyte-originating species. A simplified kinetic model of the process including only surface kinetic steps has been found to reproduce successfully both the steady-state and the small-amplitude AC response of the studied materials. The kinetic parameters of the model are determined and their relevance regarding the influence of the alloy and electrolyte composition on the relative importance of the two parallel pathways is discussed. The experimental data and model calculations indicate that the effect of acetic acid on the reaction steps related to dissolution of Fe is more significant.