  A method of electron beam cooling is considered which can be used for linear
colliders. The electron beam is cooled during collision with focused powerful
laser pulse. The ultimate transverse emittances are much below those achievable
by other methods. This method is especially useful for high energy gamma-gamma
colliders. In this paper we review and analyse limitations in this method, also
discuss a new method of obtaining very high laser powers required for the laser
cooling, radiation conditions and finaly present a possible scheme for the
laser cooling of electron beams.
