  We calculate the Luscher term for recently suggested non-Abelian flux tubes
(strings). The main feature of the non-Abelian strings is the presence of
orientational zero modes associated with rotation of their color flux inside a
non-Abelian subgroup. The Luscher term is determined by the number of light
degrees of freedom on the string wordsheet. Unlike the standard \pi/12 we get
N\pi/12 for non-Abelian strings in the U(N) gauge theories. Thus, the Luscher
coefficient acquires a dependence on the rank of the gauge group. In the models
with non-Abelian strings discussed in the literature there are two distinct
scales: the string tension \xi (the string thickness \sim \xi^{-1/2}) and the
dynamical scale of strong interactions \Lambda. At weak coupling
\xi\gg\Lambda^2. The Luscher term for non-Abelian strings experiences a jump:
at \xi^{-1/2}\ll L\ll \Lambda^{-1} it is N\pi/12 while at at L\gg \Lambda^{-1}
the orientational moduli are frozen out and the Luscher coefficient approaches
its "Luscher" value \pi/12. We raise the question of possible extra (i.e.
non-translational) light moduli on the worldsheet of QCD strings at large N.
