Transverse emittance control in linear colliders

After recalling the reasons for high brighness beams in linear colliders, the question of the preservation of the transverse emittances over long distances and in the presence of perturbations is dealt with. In both single-bunch and multi-bunch modes, the possible remedies and correction means studied so far are surveyed and discussed for the different linacs envisaged. These means raise confidence that the transverse emittances can be controlled in spite of the difficulties.