This paper analyzes the asymmetric long memory volatility dependency of the interday prices of Composite Index (CI) at Bursa Malaysia by using GARCH family models. The GARCH type models are used with the assumption that the innovations series follow either one of the following distributions: Gaussian, Student -t and skewed Student -t. The stock returns' long memory dependency is determined using the Hurst parameter. The long memory and asymmetric volatility are modelled by fractionally integrated GARCH models. It is found that the asymmetric and long memory GARCH models with skewed student-t distribution give better predictive ability on the volatility of the Kuala Lumpur Composite Index (KLCI).