We study the properties of˚-cofinitely radical supplemented modules, or, briefly, cgs˚-modules. It is shown that a module with summand sum property (SSP) is cgs˚if and only if M=w Loc˚M .w Loc˚M is the sum of all w-local direct summands of a module M / does not contain any maximal submodule, that every cofinite direct summand of a UC-extending cgs˚-module is cgs˚; and that, for any ring R; every free R-module is cgs˚if and only if R is semiperfect.
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