The heating of magnetically closed structures (loops) in the solar cor
ona by the resonant absorption of incident waves is studied by means o
f numerical simulations in the framework of nonlinear resistive magnet
ohydrodynamics (MHD). It is shown that the dynamics in the resonant la
yer is indeed very nonlinear for typical coronal parameters. The effec
t of the nonlinearity on the efficiency of the resonant heating mechan
ism is investigated. It turns out that this heating mechanism may be l
ess efficient than concluded from the linear MHD studies. As a matter
of fact, the modification of the background magnetic field results in
a shift of the resonance positions in time which in turn yields broade
r dissipation layers.