  We prove the asymptotic stability of standing kink for the nonlinear
relativistic wave equations of the Ginzburg-Landau type in one space dimension:
for any odd initial condition in a small neighborhood of the kink, the
solution, asymptotically in time, is the sum of the kink and dispersive part
described by the free Klein-Gordon equation. The remainder converges to zero in
a global norm. Crucial role in the proofs play our recent results on the
weighted energy decay for the Klein-Gordon equations.
