  Explicit expressions for the generators of the quantum superalgebra
$U_q[gl(n/m)]$ acting on a class of irreducible representations are given. The
class under consideration consists of all essentially typical representations:
for these a Gel'fand-Zetlin basis is known. The verification of the quantum
superalgebra relations to be satisfied is shown to reduce to a set of
$q$-number identities.
