In this study, we examined the long memory property of conditional variance of the BIST100 and the BOVESPA indexes considering the existence of structural breaks in the series. Results of the study will also be important from the Efficient Market Hypothesis perspective. Empirical analysis was conducted via FIGARCH, HYGARCH, GPH and modified GPH method of Phillips. As the results may be spurious in the existence of structural breaks, we performed all long memory tests before and after the Bai-Perron multiple structural breaks analysis. The sequential method of Bai-Perron multiple structural breaks analysis indicated 3 and 4 breaks for the BIST100 and the BOVESPA indexes, respectively. By considering this information we adjusted both index returns following the method of Choi et al. (2010) and performed the previous tests once again. According to the final results, conditional variance of both indexes have long memory property, that is, both of index volatilities are foreseeable under the past price information. This information conflicts with the weak form of the Efficient Market Hypothesis.