Abstract: Given two graded rings R=_x∈MR_x, A= _x∈MA_x and one graded bimodule V=_RV_A= _x∈MV_x we can obtain a graded trigangular matrix ring T. In this paper are discussed the property relations among R,A and T for graded strongly π-regularity, weakly graded direct finiteness and some gr aded ring properties in close relationship with graded J-radical.

Key words: graded triangular matrix ring, graded strongly π-regu larity, graded direct finiteness, graded Jacobson radical