  We show that the discrepancy between the observed value of the muon anomalous
moment and the standard model prediction can be explained in the framework of
nonlocal theories. We compute the leading order and next to leading order
nonlocal correction to the anomalous magnetic moment $\alpha_{NL}$ and we find
that it depends on the nonlocality scale $M_f$ and the fermion mass $m_f$ as
$\alpha_{NL} \propto m_f^2/M_f^2$. Such a dependence of the anomalous magnetic
momentum allows to explain, in a flavor-blind nonlocality scale, why the
observed anomalous magnetic moment of the electron is much closer to the
standard model prediction, and permits to predict a large anomaly that should
exist for the $\tau$ particle. We also determine the lower bounds on the
nonlocality scale, for both flavor-blind and flavor-dependent scenarios.
