ABSTRACT In recent years, the family of fractionally differenced processes has received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer ARMA (GARMA) with the Long Memory (LM), GARCH and SV components. The existence and uniqueness of second order solutions will be established. Various new results associated with this class will be reported. A simulation study has been added. A potential application will be discussed to justify the usefulness of this new class in financial modelling. *Joint work with Manabu Asai, Faculty of Economics, Soka University, Hachioji-shi, Tokyo, Japan.