  We derive maps relating currents and their divergences in non-abelian U(N)
noncommutative gauge theory with the corresponding expressions in the ordinary
(commutative) description. For the U(1) theory, in the slowly-varying-field
approximation, these maps are also seen to connect the star-gauge-covariant
anomaly in the noncommutative theory with the standard Adler--Bell--Jackiw
anomaly in the commutative version. For arbitrary fields, derivative
corrections to the maps are explicitly computed up to O(\theta^2).
