This study implements a regular vine copula methodology to evaluate the level of contagion among the exchange rates of six Latin American countries (Argentina, Brazil, Chile, Colombia, Mexico, and Peru) from June 2005 to April 2012. We measure contagion in terms of tail dependence coefficients, following Fratzscher's (1999) definition of contagion as interdependence. Our results indicate that these countries are divided into two blocks. The first block consists of Brazil, Colombia, Chile, and Mexico, whose exchange rates exhibit the largest dependence coefficients, and the second block consists of Argentina and Peru, whose exchange rate dependence coefficients with other Latin American countries are low. We also found that most of the Latin American exchange rate pairs exhibit asymmetric behaviors characterized by nonsignificant upper tail dependence and significant lower tail dependence. These results imply that there exists contagion in Latin American exchange rates in periods of large appreciations, whereas there is no evidence of contagion during periods of currency depreciation. This empirical regularity may reflect the “fear of appreciation” in emerging economies identified by Levy‐Yeyati, Sturzenegger, and Gluzmann (2013). (JEL C32, C51, E42)