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.
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