  We study the theory of noncommutative U(N) Yang-Mills field interacting with
scalar and spinor fields in the fundamental and the adjoint representations. We
include in the action both the terms describing interaction between the gauge
and the matter fields and the terms which describe interaction among the matter
fields only. Some of these interaction terms have not been considered
previously in the context of noncommutative field theory. We find all
counterterms for the theory to be finite in the one-loop approximation. It is
shown that these counterterms allow to absorb all the divergencies by
renormalization of the fields and the coupling constants, so the theory turns
out to be multiplicatively renormalizable. In case of 1PI gauge field functions
the result may easily be generalized on an arbitrary number of the matter
fields. To generalize the results for the other 1PI functions it is necessary
for the matter coupling constants to be adapted in the proper way. In some
simple cases this generalization for a part of these 1PI functions is
considered.
