To study the nature of magnetohydrodynamic (MHD) kink waves, the temporal behaviour of an initial kink perturbation of a typical coronal flux tube has been investigated in this paper. The flux tube has a transitional layer that separates the core region of the tube from the surrounding environment. In the transitional layer, the background density and magnetic field varies continuously from the internal to the external values. The magnetic field is straight and aligned with the tube axis in the internal and external regions of the flux tube, but is assumed to be twisted in the transitional layer. Hence, in the transitional layer the background Alfv´en speed is inhomogeneous and perturbations become out of phase due to the process of phase mixing. Our result shows that as the energy of the wave transfers to the local Alfv´en waves in the inhomogeneous region, the magnetic tension force becomes the dominant restoring force of the wave. The numerical results show that the nature of the small-scale oscillations in the transitional layer is determined by the ratio of the azimuthal components of the restoring forces.
