The literature on demand-driven growth models, while an important contribution to comparative political economy, places too much emphasis on developed countries and too little on the international political economic context. To extend these models to the periphery, where international influence is especially important, it is suggested that theories of hegemony and dependency be incorporated into the analysis. The main argument is that international relationships can limit the ability of peripheral countries to produce more sophisticated goods and attain high-income status. The nature of the limits varies with the needs of the hegemon (or rising hegemon), which are met via three dependency mechanisms: markets, leverage, and linkage. The proposed approach is illustrated by a study of Latin America from 1990 to 2020. After following a consumption-led model from the end of WWII until the debt crisis of the 1980s, a new export-led model was introduced in the 1990s, with different variants in the northern and southern parts of the hemisphere and different “winners” and “losers.” In the 1990s, US dominance favored Mexico through its incorporation into US industrial value chains, while China’s entrance into the region after 2000 privileged South America’s commodity producers. The trade and financial advantages afforded the two subregions by the respective powers were offset by negative aspects of the dependent relationships. Mexico’s sophisticated industries financed by US FDI benefited only certain enclaves in the country, while South America suffered reprimarization and deindustrialization through its new links with China.