  We discuss nonplanar anomalies in noncommutative gauge theories. In
particular we show that a nonplanar anomaly exists when the external
noncommutative momentum is zero and that it leads to a non-conservation of the
associated axial charge. In the case of nonplanar local anomalies, a
cancellation of the anomaly can be achieved by a Green-Schwarz mechanism. In an
example of D3 branes placed on orbifold singularity that leads to a chiral
theory, the mechanism involves twisted RR fields which propagate with zero
noncommutative momentum. Global anomalies are not cancelled and, in particular,
the decay pi0 --> 2 gamma is allowed.
