Electroweak global strings with flux tubes

We show that for a large range of parameters in a SU(2${)}_{\mathit{L}}$×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 Ũ(1) symmetry, these flux tubes become topologically stable. These results are automatically valid even if Ũ(1) is gauged.