In this paper we introduce the concept of Mori module. An R-module M is said to be a Mori module if it satisfies the ascending chain conditon on divisorial submodules. Then we introduce a new class of modules which is closely related to the class of Mori modules. Let R be a commutative ring with identity and set H={M | M is an R-module and Nil(M) is a divided prime submodule of M}. For an R-module M∈H, set T=(R\setminus Z(M))∩ (R\setminus Z(R)),
\mathfrak{T}(M)=T^-1(M),
P:=[Nil(M):_RM]. In this case the mapping Φ:\mathfrak{T}(M)⟶ M_P given by Φ(x/s)=x/s is an R-module homomorphism. The restriction of Φ to M is also an R-module homomorphism from M in to M_P given by Φ(m/1)=m/1 for every m∈ M. A nonnil submodule N of M is Φ-divisorial if Φ(N) is divisorial submodule of Φ(M). An R-module M∈ H is called Φ-Mori module if it satisfies the ascending chain condition on Φ-divisorial submodules. This paper is devoted to study the properties of Φ-Mori modules.