For a sample of six countries with dirty/free float regimes over 1999-2002 - the United States, Japan, the Czech Republic, Poland, Switzerland, and the United Kingdom, we investigate whether paired currencies exhibit a pattern of asymptotic dependence on the euro. That is, whether an extremely large appreciation or depreciation in the nominal exchange rate of one country might transmit to the euro, and vice versa. In addition, we investigate whether stock markets of European countries, outside the Euro zone, have exhibited extreme-value dependence on their exchange rates against the euro. In general, after controlling for volatility clustering and inertia in returns, we do not find evidence of extreme-value dependence either between paired exchange rates or between paired stock indices and exchanges rates. However, for asymptotic independent paired returns, we find that tail dependency of exchange rates is stronger under large appreciations than under large depreciations. In addition, we find a weak association between large currency depreciations and declining stock prices.