Understanding the evolution of volatility on the financial markets is essential for the comprehension and for the analysis of risk. This paper regards the topic of persistence of volatility in the exchange rates for four Central and Eastern European countries: Czech Republic, Hungary, Poland, and Romania. Persistence in volatility shows how quickly financial markets forget large volatility shocks. The persistence of volatility is addressed as the presence of long-term memory in the second order moment of returns and in absolute returns. The main feature of a long-memory process is that its autocorrelation function decays slower than that of a short memory process, but faster than that of an integrated one. The paper also concerns the implications on risk assessment of detecting long-term memory in the volatility of the exchange rate.