  In a model that supports both Abelian (Abrikosov-Nielsen-Olesen) and
non-Abelian strings we analyze the parameter space to find examples in which
these strings not only coexist but are degenerate in tension. We prove that
both solutions are locally stable, i.e there are no negative modes in the
string background. The tension degeneracy is achieved at the classical level
and is expected to be lifted by quantum corrections. The set up of the model,
analogous to that of Witten's superconducting cosmic strings, had been extended
to include non-Abelian strings.
