This study investigates extreme tail risks in financial markets of the euro-candidate countries and their implications for monetary policies. Our empirical tests show the prevalence of extreme risks in the conditional volatility series of selected financial variables, that is, interbank rates, equity market indexes and exchange rates. We argue that excessive instability of key target and instrument variables should be mitigated by monetary policies. Central banks in these countries will be well-advised to use both standard and unorthodox (discretionary) tools of monetary policy while steering their economies out of the financial crisis and through the euro-convergence process.