  We construct a simple class of exact solutions of the electroweak theory
including the naked $Z$--string and fermion fields. It consists in the
$Z$--string configuration ($\phi,Z_\theta$), the {\it time} and $z$ components
of the neutral gauge bosons ($Z_{0,3},A_{0,3}$) and a fermion condensate
(lepton or quark) zero mode. The $Z$--string is not altered (no feed back from
the rest of fields on the $Z$--string) while fermion condensates are zero modes
of the Dirac equation in the presence of the $Z$--string background (no feed
back from the {\it time} and $z$ components of the neutral gauge bosons on the
fermion fields). For the case of the $n$--vortex $Z$--string the number of zero
modes found for charged leptons and quarks is (according to previous results by
Jackiw and Rossi) equal to $|n|$, while for (massless) neutrinos is $|n|-1$.
The presence of fermion fields in its core make the obtained configuration a
superconducting string, but their presence (as well as that of
$Z_{0,3},A_{0,3}$) does not enhance the stability of the $Z$--string.
