Let R be a non zero ring with identity and let M be a non zero module over R. An
R-module M is called cosingular if Z*(M)=M where Z*(M)={m ∈ M, mR<<E(M)},
in this paper we introduce the concept that an R-module M is weak-cosingular if
Z*(M)≤e M. and we call that an R-module has (weak-S*)property if every submodule
N of M contains a direct summand K of M such that K≤N and N/K is weakcosingular.
And we study the properties of this kind of modules, and the relation
between this modules and other kind of modules.