  A linear stability analysis of twisted flux-tubes (strings) in an SU(2)
semilocal theory -- an Abelian-Higgs model with two charged scalar fields with
a global SU(2) symmetry -- is carried out. Here the twist refers to a relative
phase between the two complex scalars (with linear dependence on, say, the $z$
coordinate), and importantly it leads to a global current flowing along the the
string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO)
solution embedded in the semilocal theory. Our numerical investigations of the
small fluctuation spectrum confirm previous results that twisted strings
exhibit instabilities whose amplitudes grow exponentially in time. More
precisely twisted strings with a single magnetic flux quantum admit a
continuous family of unstable eigenmodes with harmonic $z$ dependence, indexed
by a wavenumber $k\in[-k_{\rm m},k_{\rm m}]$. Carrying out a perturbative
semi-analytic analysis of the bifurcation, it is found that the purely
numerical results are very well reproduced. This way one obtains not only a
good qualitative description of the twisted solutions themselves as well as of
their instabilities, but also a quantitative description of the numerical
results. Our semi-analytic results indicate that in close analogy to the known
instability of the embedded ANO vortex a twisted string is also likely to
expand in size caused by the spreading out of its magnetic flux.
