The first nonlinear study of the instability of the resonant absorption is presented in this paper. The nonlinear evolution of the resonant absorption of Alfv¿n waves in an inhomogeneous plasma is studied via solution of the time-dependent 3-D, low-&bgr;, resistive MHD equations. Highly sheared velocities that are subject to the Kelvin-Helmholtz like instability are found at the narrow dissipation layers. Three dimensional Kelvin-Helmholtz like vortices appear at and near dissipation layers and propagate along the slab of plasma. The narrow resonant heating layers are deformed by the self-consistent shear flow. In the solar active regions where the resonant absorption of Alfv¿n waves is believed to occur the instability may lead to turbulent enhancement of the dissipation parameters and account for the observed turbulent velocities inferred from the non-thermal broadening of x-ray and EUV emission lines. ¿ American Geophysical Union 1994