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One commonly believes that international markets are more dependent during a crisis than they are are in more tranquil times. This extra dependence is often referred to as contagion between markets. We present a definition of contagion between financial markets based on local correlation and propose a test to detect the presence of contagion. The test does not require the specification of crisis and normal periods. As such, it avoids difficulties associated with testing for correlation breakdown, such as hand picking subsets of the data, and it provides a better understanding of the degree of dependence between financial markets. Using this test, we find evidence of contagion between developed and U.S. equity markets and evidence of flight to quality from the U.S. equity market to the U.S. government bond market. The practical application of the test involves nonparametric estimation techniques. This is joint work with Brendan Bradley.