  Classical solutions describing strings endowed with an electric charge and
carrying a constant electromagnetic current are constructed within the bosonic
sector of the Electroweak Theory. For any given ratio of the Higgs boson mass
to W boson mass and for any Weinberg's angle, these strings comprise a family
that can be parameterized by values of the current through their cross section,
$I_3$, by their electric charge per unit string length, $I_0$, and by two
integers. These parameters determine the electromagnetic and Z fluxes, as well
as the angular momentum and momentum densities of the string. For $I_0\to 0$
and $I_3\to 0$ the solutions reduce to Z strings, or, for solutions with
$I_0=\pm I_3$, to the W-dressed Z strings whose existence was discussed some
time ago.
