  There are observational evidences for the existence of 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. To 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 Alfv\'{e}n continuum modes and the
decay rate of the global kink oscillation depending on the twist model and the
sign of the longitudinal ($k_z$) 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 $k_z$ 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 cascade to small scales.
