This paper seeks to explain, from the perspective of economic sociology, the Argentinean process of convertibility as a form of establishing the sovereignty of currency. Through the analysis of parliamentary debates on the adoption of the law, the logic and implications of a currency created “forever,” as its promoters hoped, are studied. The idea of a sovereign currency, whose model makes it possible to envisage monetary forms with nominal anchors and a certain type of associated crises, is also discussed.