Normal Bundles, Pfaffians and Anomalies

We deal with the problem of diffeomorphism anomaly in theories with branes. In particular we thoroughly analyze the problem of the residual chiral anomaly of a five-brane immersed in M-theory, paying attention to its global formulation in the five-brane world-volume. We conclude that the anomaly can be canceled by a {\it local} counterterm in the five-brane world-volume.