We examine current-carrying configurations of cosmic strings in non-Ab
elian gauge theories. We study the solutions numerically and point out
that the currents will be at best dynamically stable and not subject
to any topological quantization or conservation, as in conventional mo
dels of string superconduction. We suggest that non-Abelian string loo
ps may be unable to support persistent currents in the absence of exte
rnal fields. This will have relevance to vorton stability.