  The elastic light-light scattering below the threshold of the $e^+e^-$ pair
production leads to a variation in polarization of hard $\gamma$-quanta
traversing without loss a region where the laser light is focused. Equations
are obtained which determine the variation of Stokes parameters of
$\gamma$-quanta in this case, and their solutions are given. It is pointed out
that this effect can be observed in the experiment E-144 at SLAC. It should be
taken into account (and, perhaps, it can be used) in experiments at future
$\gamma \gamma$ colliders.
