  We first consider M-theory formulated on an open eleven-dimensional
spin-manifold. There is then a potential anomaly under gauge transformations on
the E_8 bundle that is defined over the boundary and also under diffeomorphisms
of the boundary. We then consider M-theory configurations that include a
five-brane. In this case, diffeomorphisms of the eleven-manifold induce
diffeomorphisms of the five-brane world-volume and gauge transformations on its
normal bundle. These transformations are also potentially anomalous. In both of
these cases, it has previously been shown that the perturbative anomalies, i.e.
the anomalies under transformations that can be continuously connected to the
identity, cancel. We extend this analysis to global anomalies, i.e. anomalies
under transformations in other components of the group of gauge transformations
and diffeomorphisms. These anomalies are given by certain topological
invariants, that we explicitly construct.
