Abstract
We show that for a large range of parameters in a SU(2${)}_{\mathit{L}}$\ifmmode\times\else\texttimes\fi{}U(1) electroweak theory with two Higgs doublets there may exist classically stable flux tubes of Z boson magnetic field. In a limit of an extra global \ifmmode \tilde{U}\else \~{U}\fi{}(1) symmetry, these flux tubes become topologically stable. These results are automatically valid even if \ifmmode \tilde{U}\else \~{U}\fi{}(1) is gauged.
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