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This study applies a quantile cointegration model to investigate if COVID-19 outbreaks in the BRICS (China, India, Russia, Brazil, and South Africa) and the United States have a long-run equilibrium relationship with the dynamics of oil prices. (1) The standard cointegration models are unstable, indicating the possibility of structural breaks and nonlinearity in the relationship between the COVID-19 pandemic and oil prices; (2) The results of the quantile cointegration model suggest the COVID-19 pandemic and oil prices are nearly cointegrated over whole quantiles of the oil price distribution for the United States, Russia, South Africa, and Brazil. However, the long-run equilibrium relationship between the COVID-19 pandemic and oil prices in China is more likely to occur in the lower quantiles of the oil price distribution; (3) For India, the equilibrium link exists only across the two higher quantiles (0.7 and 0.8 quantiles) of the oil price distribution. Finally, our research has significant policy implications for the governments of the world's largest countries that are concerned about the impact of the COVID-19 pandemic outbreak on oil prices. [ABSTRACT FROM AUTHOR]