  We define a nonabelian particle-vortex duality as a $3-$dimensional analogue
of the usual $2-$dimensional worldsheet nonabelian T-duality. The
transformation is defined in the presence of a global $SU(2)$ symmetry and,
although derived from a string theoretic setting, we formulate it generally. We
then apply it to so-called "semilocal strings" in an $SU(2)_{G}\times U(1)_{L}$
gauge theory, originally discovered in the context of cosmic string physics.
