  The present paper reviews recent advances in the theory of nonlinear driven
magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple
estimations show that in the vicinity of resonant positions the amplitude of
variables can grow over the threshold where linear descriptions are valid.
Using the method of matched asymptotic expansions, governing equations of
dynamics inside the dissipative layer and jump conditions across the
dissipative layers are derived. These relations are essential when studying the
efficiency of resonant absorption. Nonlinearity in dissipative layers can
generate new effects, such as mean flows, which can have serious implications
on the stability and efficiency of the resonance.
