In this study we tested the existence of long memory in the the return series for major Central Eastern European and Balkans stock markets, using the following statistical methods: Hurst Exponent, GPH method, Andrews and Guggenberger method, Reisen method, Willinger, Taqqu and Teverovsky method and ARFIMA model. The results obtained are mixed. The Hurst Exponent showed the existence of long memory in all indices, except PX. After applying the GPH method, the results showed that BET, ATHEX, SOFIX and CROBEX have a predictable behavior. The ARFIMA model results support the existence of long memory for BUX, SAX and BELEX. The predictable behavior of index returns may suggest that the CEE and Balkans stock markets are not weak form efficient.