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This paper examines the dependence structure between the emerging stock markets of the BRICS countries and influential global factors. Using the quantile regression approach, our results for the period from September 1997 to September 2013 show that the BRICS stock markets exhibit dependence with the global stock and commodity markets (S&P index, oil, and gold) as well as changes in the U.S. stock market uncertainty (CBOE Volatility Index). This dependence structure is often asymmetric and affected by the onset of the recent global financial crisis. By contrast, the U.S. economic policy uncertainty has no impact on the BRICS stock markets.