  We investigate the graded Brown--McCoy and the classical Brown--McCoy radical
of a graded ring, which is the direct sum of a family of its additive subgroups
indexed by a nonempty set, under the assumption that the product of homogeneous
elements is again homogeneous. There are two kinds of the graded Brown--McCoy
radical, the graded Brown--McCoy and the large graded Brown--McCoy radical of a
graded ring. Several characterizations of the graded Brown--McCoy radical are
given, and it is proved that the large graded Brown--McCoy radical of a graded
ring is the largest homogeneous ideal contained in the classical Brown--McCoy
radical of that ring.
