  The electromagnetic dipole moments of the tau lepton and the
chromoelectromagnetic dipole moments of the top quark are estimated via
flavor-changing neutral currents, mediated by a new neutral massive gauge
boson. We predict them in the context of models beyond the Standard Model with
extended current sectors, in which simple analytic expressions for the dipole
moments are presented. For the different $Z^\prime$ gauge boson considered, the
best prediction for the magnetic dipole moment of the tau lepton, $|a_\tau|$,
is of the order of $10^{-8}$, while the highest value for the electric one,
$|d_\tau|$, corresponds to $10^{-24}$ $e\,$cm; our main result for the
chromomagnetic dipole moment of the top quark, $|\hat{\mu}_t|$, is $10^{-6}$,
and the value for the chromoelectric one, $|d_t|$, can be as high as $10^{-22}$
$e\,$cm. We compare our results, revisiting the corresponding Standard Model
predictions, in which the chromomagnetic dipole moment of the top quark is
carefully evaluated, finding explicit imaginary contributions.
