We investigate the problem of anisotropy damping in the Kasner cosmological
spacetime by bosonic strings. It is shown that bosonic strings can account
under proper circumstances, for the anisotropy damping that may took place
in the primordial stages of the evolution of the universe, which resulted
in the highly homogeneous and isotropic present phase. Assuming that at the
verge of the initial singularity (t = 0), quantum effects resulted in the
production of particles, which lire string-like structures, anisotropy damp
ing is then a possible outcome. This is also verified by qualitative and qu
antitative arguments in the case where one considers the full back-reaction
problem. (C) 1998 Elsevier Science B.V. All rights reserved.