There is observational evidence for the existence of a twisted magnetic field in the solar corona. This inspires us to investigate the effect of a twisted magnetic field on the evolution of magnetohydrodynamic (MHD) kink waves in coronal loops. With this aim, we solve the incompressible linearized MHD equations in a magnetically twisted nonuniform coronal flux tube in the limit of long wavelengths. Our results show that a twisted magnetic field can enhance or diminish the rate of phase mixing of the Alfvén continuum modes and the decay rate of the global kink oscillation depending on the twist model and the sign of the longitudinal (kz) and azimuthal (m) wavenumbers. Also, our results confirm that in the presence of a twisted magnetic field, when the sign of one of the two wavenumbers m and kz is changed, the symmetry with respect to the propagation direction is broken. Even a small amount of twist can have an important impact on the process of energy cascading to small scales.
