  We study the perturbative unitarity of non-commutative quantum Yang-Mills
theories, extending previous investigations on scalar field theories to the
gauge case where non-locality mingles with the presence of unphysical states.
We concentrate our efforts on two different aspects of the problem. We start by
discussing the analytical structure of the vacuum polarization tensor, showing
how Cutkoski's rules and positivity of the spectral function are realized when
non-commutativity does not affect the temporal coordinate. When instead
non-commutativity involves time, we find the presence of extra troublesome
singularities on the $p_0^2$-plane that seem to invalidate the perturbative
unitarity of the theory. The existence of new tachyonic poles, with respect to
the scalar case, is also uncovered. Then we turn our attention to a different
unitarity check in the ordinary theories, namely time exponentiation of a
Wilson loop. We perform a $O(g^4)$ generalization to the (spatial)
non-commutative case of the familiar results in the usual Yang-Mills theory. We
show that exponentiation persists at $O(g^4)$ in spite of the presence of Moyal
phases reflecting non-commutativity and of the singular infrared behaviour
induced by UV/IR mixing.
