This paper examines the long memory properties in both the returns and volatility of Korean stock prices. For this purpose, the ARFIMA-FIGARCH model was applied to the daily KOSPI and KOSDAQ return series. In the data analysis, the ARFIMA-FIGARCH model establishes the robustness of long memory results, although the presence of long memory is questionable in the returns of two daily indices. In addition, the assumption of non-normality is appropriate for capturing the asymmetry and tail fatness of estimated residuals. These findings suggest that the model based on the Gaussian normality assumption may be inappropriate for modeling the long memory property. Finally, the presence of long memory in the Korean stock market is not spurious as a result of market structural changes.