In this paper, we define the concept of generalized cubic subsemigroups (ideals) of a semigroup and investigate some of its related properties. In particular, we introduce the concept of (∈ ( γ 1 ,γ 2 ) , ∈ ( γ 1 ,γ 2 ) ∨q ( δ 1 ,δ 2 ) )-cubic ideal, (∈ ( γ 1 ,γ 2 ) , ∈ ( γ 1 ,γ 2 ) ∨q ( δ 1 ,δ 2 ) )-cubic quasi-ideal, (∈ ( γ 1 ,γ 2 ) , ∈ ( γ 1 ,γ 2 ) ∨q ( δ 1 ,δ 2 ) )-cubic bi-ideal and (∈ ( γ 1 ,γ 2 ) , ∈ ( γ 1 ,γ 2 ) ∨q ( δ 1 ,δ 2 ) )-cubic prime/semiprime ideal of a semigroup.