We outline the ideas of approximately 2-absorbing and weakly approximately 2-absorbing submodules and list the fundamental characteristics of these submodule classes. This is a generalization of prime and weakly prime sub-modules. Let A be a T-module and T a commutative ring. Weakly prime is the state in which a proper submodule U of A is when a, b ∈ T and m ∈ A, bam ∈ U implies that am ∈ U or bm ∈ U. When a, b within T, m in A and abm ∈ U then a proper submodule U of A is said to be approximately 2-absorbing (or weakly approximately 2-absorbing sub-modules). If a, b, ∈ T A m ∈ A, and abm ∈ U (resp.0≠abm ∈ U), then then a2 m ∈ N or b2 m ∈ N or a2 b2 ∈ (U:A).