  We study anomalies of six-dimensional gauge theories compactified on
orbifolds. In addition to the known bulk anomalies, brane anomalies appear on
orbifold fixpoints in the case of chiral boundary conditions. At a fixpoint,
where the bulk gauge group G is broken to a subgroup H, the non-abelian
G-anomaly in the bulk reduces to a H-anomaly which depends in a simple manner
on the chiral boundary conditions. We illustrate this mechanism by means of a
SO(10) GUT model.
