  Using path integral method (Fujikawa's method) we calculate anomalies in
noncommutative gauge theories with fermions in the bi-fundamental and adjoint
representations. We find that axial and chiral gauge anomalies coming from
non-planar contributions are derived in the low noncommutative momentum limit
$\widetilde{p}^{\mu}(\equiv \theta^{\mu\nu}p_{\nu}) \to 0$. The adjoint chiral
fermion carries no anomaly in the non-planar sector in $D=4k (k=1,2,...,)$
dimensions. It is naturally shown from the path integral method that anomalies
in non-planar sector originate in UV/IR mixing.
