Let R be a graded ring.The concepts of weak Gorenstein gr-projective modules,gr-injective modules and gr-flat modules are introduced,and some homological characterizations of weak Gorenstein gr-projective mod-ules are given.It is shown that a weak Gorenstein gr-projective module is a Gorenstein gr-projective R-module over a graded n-Gorenstein ring R.Moreover,it is proved that:if any graded injective R-module has a finite graded flat dimension,then a graded module M is weak Gorenstein gr-flat if and only if M is Gorenstein gr-flat.
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