In this paper, we introduce new classes of submodules and modules named small approximately 2-absorbing submodules and modules which are new generalization of small prime submodule and small prime module. A proper submodule N of M is said to be small approximately 2-absorbing submodules (res Small approximately 2-absorbing Module) if when a, b ∈ R and < m > ≪M, abm ∈  N implies that a2 ∈N or b2 m∈N or a2 b2∈ (N : M) (res if < 0 > is a small approximately 2-absorbing submodule of M, such that if abm ∈ and ≪M, then a2 m = 0 or b2 m = 0 or (ab)2 ∈ annM). Also, give various results and properties of this concepts.