  We study the effects of an anomalous Z' boson on the anomalous magnetic
moment of the muon (g-2), and especially the impact of its axial coupling. We
mainly evaluate the negative contribution to (g-2) of such couplings at
one-loop and look at the anomalous couplings generated at two loops. We find
areas of the parameter space, where the anomalous contribution becomes
comparable and even dominant compared to the one-loop contribution. We show
that in such cases, the cutoff of the theory is sufficiently low, so that new
charged fermions can be found in the next round of collider experiments. We
comment on the realization of such a context in string theory orientifolds.
