We consider slow resonant MHD waves in 1D planar equilibria with the unidirectional magnetic field. A nonlinear equation governing this waves in a slow resonant layer is derived. A periodic solution in the form of propagating wave with a permanent shape is found in the limiting case, where nonlinearity dominates dissipation. This solution is used to derive a connection formula that connects the values of the normal component of the velocity at two sides of the resonant layer. This connection formula is, in turn, used to study the interaction of an incoming sound wave with a slab containing an inhomogeneous magnetized plasma. The coefficient of the wave energy resonant absorption is calculated and compared with its counterpart obtained on the basis of linear theory. ©2000 American Institute of Physics.