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It is highly probable that the fulfillment of the exchange rate stability convergence criterion (ERSC) in the European Union (EU) New Member States (NMS) will be evaluated within the asymmetric fluctuation bank around the central parity. Obviously, there is a necessity for analysis of the asymmetric effects in the NMS and candidate countries exchange rate volatility. In this article, the TARCH model extended by the concept of implicit target exchange rate is applied on daily data from seven NMS and candidate countries. The results suggest that symptoms of asymmetry were found in volatility of almost all exchange rates while some pose a potential threat to fulfillment of the criterion. By contrast, the most positive results were revealed in Slovakia where the increase in the exchange rate volatility is driven by the appreciation of the national currency and the appreciation-side deviation from the target exchange rate. Such a finding is consistent with the asymmetric fluctuation band which allows substantially larger deviations on the appreciation side. [ABSTRACT FROM AUTHOR]