  A nonabelian generalization of the neutral Witten current-carrying string
model is discussed in which the bosonic current-carrier belongs to a two
dimensional representation of SU(2). We find that the current-carrying
solutions can be of three different kinds: either the current spans a U(1)
subgroup, and in which case one is left with an abelian current-carrying
string, or the three currents are all lightlike, travelling in the same
direction (only left or right movers). The third, genuinely nonabelian
situation, cannot be handled within a cylindrically symmetric framework, but
can be shown to depend on all possible string Lorentz invariant quantities that
can be constructed out of the phase gradients.
