Summary: A well-known generalization of a semigroup \(S\) is called the \(\Gamma\)-semigroup. We generalize the notion of biacts over semigroups to \(\Gamma\)-biacts over \(\Gamma\)-semigroups. Green’s relations on semigroups and biacts play an important role in these theories. In this paper, we study Green’s relations on \(\Gamma\)-biacts.