Aims.We study kink waves in a magnetic flux tube modelled as a straight core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field, and derive the dispersion relation for this configuration.\ud Methods.The existence and behaviour of the kink modes are examined with specific attention to the effect that the addition of magnetic twist has on phase speeds and periods. Analytic expansions to the short and long wavelength approximations are also considered.\ud Results.The magnetic twist is found to introduce of an infinite set of body modes into solutions of the dispersion relation not present in the untwisted case. Moreover, for the kink modes, the width of interval of this infinite set, generally found to occupy phase speeds around the annulus' longitudinal Alfvén speed, increases for longer wavelengths. Two surface modes are also present in the solution, one at each surface: the internal and the external edges of the annulus. The magnetic twist is found to increase or decrease the phase speeds of these surface modes that are depending on the ratio of internal and external Alfvén speeds in the flux tube.\ud Conclusions.The magnetic twist of the annulus region of a flux tube is found to have a marked effect on the phase speeds of occurring modes. A straight annulus layer increased (or decreased) the periods of the surface modes for a tube modelled as a density (magnetic) enhancement. The addition of twist reduces the periods of the modes in both cases
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