The present day theory of ideals has been standardized in some respects, and it is recently being extensively enriched and studied by many algebraists. This notion of ideals that was originally formulated by Dedekind for the ring of integers of an algebraic number eld, was again generalized by Emmy Noether in terms of one-sided and two-sided ideals in associative rings. Subsequently, this theory of ideals has won universal acceptance due to its signi cance in characterizing dierent algebraic structures as is evident from the vast litera- ture available on the topic. Further, Steinfeld[22 and 23] invented quasi-ideals of rings and semigroups in 1953 and in 1956 respectively as a generalization of one-sided ideals of rings and semigroups and then in 1952, Good and Hughes  jointly announced the arrival of the bi-ideal of semigroups as a generalization of one-sided ideals of semigroups. Interestingly, the concept of bi-ideals of semigroups was given earlier than the concept of quasi-ideals of semigroups and it was subsequently revealed that the bi-ideal of semigroups generalizes not only one-sided ideals of semigroups but also quasi-ideals of semigroups. Moreover, in 1962, the concept of the bi-ideal was extended to associative rings by Lajos . The notion of the generalized biideal[(or generalized (1,1)-ideal] was rst introduced in rings in 1970 by Szasz[3 and 4] and then in semigroups in 1984 by Lajos [15, 16, 17, 18 and 19] as a generalization of bi-ideals of rings and semigroups. In fact the notion of gamma-semigroups is a generalization of the con- cept of semigroups. For any relevant terminologies and unde ned concepts on gamma-semigroups in this paper, readers can see [6, 7 and 10]. The notion of quasi- gamma-ideals and bi-gamma-ideals in gamma-semigroups was given by Chinram[11 and 12] in 2006 and in 2007 respectively. The properties of the bi-ideal and the gener- alized bi-ideal in semigroups as well as in gamma-semigroups have been studied by several authors [1, 2, 8, 9, 20 and 21]. In this paper, we have studied some gen- eral classical properties of the generalized bi-gamma-ideal in gamma-semigroups and also the prime and irreducible generalized bi-gamma-ideal in gamma-semigroups. Further, S. Lajos  identi ed a class of semigroups for which some classes of generalized bi-ideals are distinct from the class of bi-ideals. He also raised the problem of characterizing those semigroups whose generalized bi-ideals are bi-ideals. This problem was solved by F. Catino. We have investigated it in gamma-semigroups. In fact the class of generalized bi-gamma-ideals of gamma-semigroups is a generalization of the class of generalized bi-ideals in semigroups in the same way as bi-gamma-ideals in gamma-semigroups are a generalization of bi-ideals in semigroups. For the current directions of the theory, readers can refer the reference of this paper and the references of the reference.