  Vortex solutions in the two Higgs doublet electroweak model are constructed,
and their stability to small perturbations is studied. The most general
perturbation is decomposed into angular momentum modes, the least stable mode
is identified, and the linearised energy change of the vortex under this
perturbation is calculated numerically for various choices of parameters, thus
determining whether or not the string is stable. It is found that, for
realistic values of the Higgs mass and Weinberg angle, the string is unstable.
