The propagation of shear-Alfvén waves in an incompressible plasma is considered in the vicinity of an X-line of the magnetic field. A small dissipation leads to a discrete spectrum of weakly damped MHD modes, with a dissipative layer in the vicinity of the separatrices. Finite amplitude perturbations imposed from the boundaries and propagating perpendicularly to one of the separatrices are then considered, and the characteristic timescale of their evolution is derived.