The paper examines the long memory property of stock returns and its implications using daily index returns for eight CEE emerging markets: Romania, Hungary, Czech Republic, Poland, Slovenia, Bulgaria, Slovakia, and Croatia. Several nonparametric methods for testing for long memory are employed, as well as parametric long memory models. The ARFIMA-FIGARCH model seems the most appropriate specification since the nonlinearity tests can not reject the null of independent and identically distributed residuals, implying that this specification accounts for the nonlinearity in the data. The estimated fractional differencing parameter is statistically significant in seven of the eight emerging economies employed in the study, suggesting the presence of long memory in the returns in these financial markets.