  We consider open supermembranes in eleven dimensions in the presence of
closed M-Theory five-branes. It has been shown that, in a flat space-time, the
world-volume action is kappa invariant and preserves a fraction of the eleven
dimensional supersymmetries if the boundaries of the membranes lie on the
five-branes. We calculate the reparametrisation anomalies due to the chiral
fermions on the boundaries of the membrane and examine their cancellation
mechanism. We show that these anomalies cancel with the aid of a classical term
in the world-volume action, provided that the tensions of the five-brane and
the membrane are related to the eleven dimensional gravitational constant in a
way already noticed in M-Theory.
