  We investigate the stability of the electroweak Z-string at high
temperatures. Our results show that while finite temperature corrections can
improve the stability of the Z-string, their effect is not strong enough to
stabilize the Z-string in the standard electroweak model. Consequently, the
Z-string will be unstable even under the conditions present during the
electroweak phase transition. We then consider phenomenologically viable models
based on the gauge group $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ and show
that metastable strings exist and are stable to small perturbations for a large
region of the parameter space for these models. We also show that these strings
are superconducting with bosonic charge carriers. The string superconductivity
may be able to stabilize segments and loops against dynamical contraction.
Possible implications of these strings for cosmology are discussed.
