  We investigate the structure of local anomalies of heterotic E_8 x E_8'
theory on T^6/Z_4. We show that the untwisted states lead to anomalies in ten,
six and four dimensions. At each of the six dimensional fixed spaces of this
orbifold the twisted states ensure, that the anomalies factorize separately. As
some of these twisted states live on T^2/Z_2, they give rise to four
dimensional anomalies as well. At all four dimensional fixed points at worst a
single Abelian anomaly can arise. Since the anomalies in all these dimensions
factorize in a universal way, they can be canceled simultaneously. In addition,
we show that for all U(1) factors at the four dimensional fixed points at least
logarithmically divergent Fayet--Ilopoulos tadpoles are generated.
