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We study modules with the properties and which are adopted Zöschinger’s modules with the properties and. We call a module module if has a weak-supplement in every torsion extension. Similarly if has ample weak-supplements in every torsion extension then is called module. We obtain various properties of these modules. We will show that (1) Every direct summand of a module is a module.(2) A module has the property iff every submodule of has the property.(3) Any factor module of a module is a module under a special condition.(4) Over a nonlocal ring, if every submodule of a module is a module, then it is cofinitely weak-supplemented.