The paper analyses the growth models of Argentina, Bolivia, Brazil, Chile, and Mexico since 1996. We depart from the typology proposed by Bizberg (2019) and apply a growth decomposition based on the Sraffian supermultiplier (Freitas and Dweck, 2013). We argue that the growth models perspective, introduced by Baccaro and Pontusson (2016), contributes to understanding the diversities of capitalism in Latin America. We find that the commodities boom oriented the countries towards export-led growth models, especially in Bolivia, Chile, and Mexico. Brazil and Argentina presented a hybrid growth model, with higher household consumption, and government expenditure along with exports growth. After the commodities boom, the export-led model was no longer feasible for commodity exporters. Mexico sustained the existing model, based on low-value-added manufacturing exports. Brazil and Argentina reduced public expenditures generating economic stagnation. Chile and Bolivia increased public expenditure, sustaining growth at a slower pace. This work extends the growth models perspective to emerging countries, considering former contributions of the Latin American political economy. It also highlights how the growth models evolved in tandem with changing international conditions. Finally, the paper opens a research agenda for the political economy of stagnation in Latin American economies.