  We consider initial data for the real Ginzburg-Landau equation having two
widely separated zeros. We require these initial conditions to be locally close
to a stationary solution (the ``kink'' solution) except for a perturbation
supported in a small interval between the two kinks. We show that such a
perturbation vanishes on a time scale much shorter than the time scale for the
motion of the kinks. The consequences of this bound, in the context of earlier
studies of the dynamics of kinks in the Ginzburg-Landau equation, [ER], are as
follows: we consider initial conditions $v_0$ whose restriction to a bounded
interval $I$ have several zeros, not too regularly spaced, and other zeros of
$v_0$ are very far from $I$. We show that all these zeros eventually disappear
by colliding with each other. This relaxation process is very slow: it takes a
time of order exponential of the length of $I$.
