Persistent current account imbalances are a core feature of the global economy, yet political economists lack a coherent understanding of what makes them sustainable over long periods of time. In this paper, we elaborate a theoretical framework linking current account imbalances, growth models, and international financial conditions. Our central insight is that financial (under-)development is key to sustaining current account imbalances. Specifically, deep and liquid financial markets enable the reproduction of consumption-led growth by relaxing the current account constraint, while financial underdevelopment helps export-led growth. We test our theoretical propositions with a TSCS analysis of the relationship between current account positions, export- and consumption-led growth contributions, and financial conditions in 55 countries at various levels of development observed at 5-year intervals between 1996 and 2018. Our analysis identifies an important dissimilarity in the way growth models reproduce themselves over time and in their relationship with global finance: While financial development is crucial for the long-term feasibility of consumption-led growth, financial underdevelopment is a facilitating factor for export-led growth.