We work out the one-loop U(1)A anomaly for noncommutative SU(N) gauge
theories up to second order in the noncommutative parameter θμν.
We set θ0i=0 and conclude that there is no breaking of the classical
U(1)A symmetry of the theory coming from the contributions that are either
linear or quadratic in θμν. Of course, the ordinary anomalous
contributions will be still with us. We also show that the one-loop
conservation of the nonsinglet currents holds at least up to second order in
θμν. We adapt our results to noncommutative gauge theories with
SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde