  The graded-fermion algebra and quasi-spin formalism are introduced and
applied to obtain the $gl(m|n)\downarrow osp(m|n)$ branching rules for the
"two-column" tensor irreducible representations of gl(m|n), for the case $m\leq
n (n > 2)$. In the case m < n, all such irreducible representations of gl(m|n)
are shown to be completely reducible as representations of osp(m|n). This is
also shown to be true for the case m=n except for the "spin-singlet"
representations which contain an indecomposable representation of osp(m|n) with
composition length 3. These branching rules are given in fully explicit form.
