The phase-mixing and resonant dissipation of Alfven waves is studied in both the 'closed' magnetic loops and the 'open' coronal holes observed in the hot solar corona. The resulting energry transfer from large to small length scales contributes to the heating of these magnetic structures. The non-linear 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.
Key words: nonlinear MHD, resonant dissipation, phase-mixing