In this study, I measure the dependence of the financial markets of certain emerging market countries on US monetary policy and monetary policy uncertainty. To do so, I apply the time- varying copula models proposed by Patton (200). I am particularly interested in the differences between these markets' dependence on US monetary policy, i.e. which of the countries' financial markets tend to comove in response to quantitative easing or quantitative tightening policies. The results are important because financial risks via contagion need monitoring, especially since the 2008 subprime crisis, although emerging markets were affected less than advanced economies. My analysis point to a significant difference between these emerging markets regarding their dependence on US monetary policy. The correlation persistence parameters, which determine the evolution of time-varying dependence, show that emerging countries, especially in Latin America, are strongly dependent on both US monetary policy and monetary policy uncertainty. It is therefore interesting to see that the results reveal increasing dependence during the subprime crisis but a decrease after 2009. I conclude that increasing dependence during stress periods should be considered as a risk factor for policymakers who closely monitor financial markets in emerging countries.