  The nonaxisymmetric magnetohydrodynamic (MHD) modes in a zero-beta
cylindrical compressible thin magnetic flux tube modelled as a twisted core
surrounded by a magnetically twisted annulus, both embedded in a straight
ambient external field is considered. The dispersion relation is derived and
solved analytically and numerically to obtain the frequencies of the
nonaxisymmetric MHD waves. The main result is that the twisted magnetic annulus
does affect the period ratio P_1/P_2 of the kink modes. For the kink modes, the
magnetic twist in the annulus region can achieve deviations from P_1/P_2 = 2 of
the same order of magnitude as in the observations. Furthermore, the effect of
the internal twist on the fluting modes is investigated.
