AbstractThe notion of Γ-semigroups has been introduced by M. K. Sen and N. K. Saha. The concept of (co-ordered) Γ-semigroups with apartness in Bishop’s constructive algebra was introduced by this author. Many classical notions and processes of semigroups and Γ-semigroups have been extended to (co-ordered) Γ-semigroups with apartness such as ideals, filters and the first theorem of isomorphism of this class of algebraic structures. In this paper, as a continuation of earlier research, the author designs a form of the third isomorphism theorems for Γ-semigroups and co-ordered Γ-semigroups with apartness which does not have its counterpart in the classical Γ-semigroup theory.