Chiral anomalies in noncommutative YM theories

Using cohomological methods we discuss several issues related to chiral ano malies in noncommutative U(N) YM theories in any even dimension. We show th at for each dimension there is only one solution of the WZ consistency cond ition and that there cannot be any reducible anomaly, nor any mixed anomaly when the gauge group is a product group. We also clarify some puzzling asp ects of the issue of the anomaly when chiral fermions are in the adjoint re presentation. (C) 2001 Published by Elsevier Science B.V.