The phase mixing and resonant dissipation of Alfven waves is studied i
n both the 'closed' magnetic loops and the 'open' coronal holes observ
ed in the hot solar corona. The resulting energy transfer from large t
o small length scales contributes to the heating of these magnetic str
uctures. The nonlinear simulations show that the periodically varying
shear flows that occur in the resonant layers are unstable. In coronal
holes, the phase mixing of running Alfven waves is speeded up by the
'flaring out' of the magnetic field lines in the lower chromosphere.