  It is shown that in models including the standard electroweak theory and for
some particular values of the underlying parameters, electric currents can be
spontaneously generated in cosmic strings, without the need of any external
field (e.g., electric or magnetic) as is required in most models. This
mechanism is then shown to break spontaneously the Lorentz invariance along the
initially Goto-Nambu string. The characteristic time needed for the current to
build up is estimated and found to lowest order to depend only on the mass of
the intermediate $W$ vector boson and the fine structure constant.
