  We prove a strong version of the Max-Flow Min-Cut theorem for countable
networks, namely that in every such network there exist a flow and a cut that
are "orthogonal" to each other, in the sense that the flow saturates the cut
and is zero on the reverse cut. If the network does not contain infinite trails
then this flow can be chosen to be mundane, i.e. to be a sum of flows along
finite paths. We show that in the presence of infinite trails there may be no
orthogonal pair of a cut and a mundane flow. We finally show that for locally
finite networks there is an orthogonal pair of a cut and a flow that satisfies
Kirchhoff's first law also for ends.
