In this paper, we use weekly stock market data to examine whether the volatility of stock returns of ten emerging capital markets of the new EU member countries has changed since the opening of their capital markets. In particular we are interested in understanding whether there are high and low periods of stock returns volatility and what the degree of correlation across these markets is. We estimate a Markov-Switching ARCH (SWARCH) model proposed by Hamilton and Susmel (1994) and we allow for the possibility that two or three volatility regimes may exist for stock returns volatility. The main finding of the present study is that the high volatility of stock returns of all new EU emerging stock markets is associated mainly with the 1997‒1998 Asian and Russian financial crises as well as over the 2007‒2009 financial turmoil, while there is a transition to the low volatility regime as they approach the accession to the EU in 2004. It is also shown that the capital flows liberalization process has resulted in an increase in volatility of stock returns in most cases.