  The aim of this note is to discuss, in a somewhat informal language, the
cancellation of anomalies (in topologically trivial space-time) for 5-branes
using as "building blocks": i) a generalization to p-branes of the Dirac
strings of monopoles (Dirac branes) and a refinement of this idea involving a
geometric regularization of Dirac branes, leading to the formalism of
"characteristic currents" ii) the PST formalism . As an example of the
potentiality of the developed framework we discuss in some detail the anomaly
cancellation in the D=10 effective theory of heterotic string and 5-brane
coupled to supergravity, where the anomaly inflow is automatically generated.
Some remarks are also made on a similar approach to the problem of anomaly
cancellation in the effective theory of M5-brane coupled to D=11 supergravity,
developed in collaboration with M.Tonin, where however still as open problem
remains a Dirac anomaly.
