  In this paper we examine the Cosmic No-Hair Conjecture (CNHC) in brane world
scenarios. For the validity of this conjecture, in addition to the strong and
weak energy conditions for the matter field, a similar type of assumption is to
be made on the quadratic correction term and there is a restriction on the
non-local term. It is shown by examples with realistic fluid models that strong
and weak energy conditions are sufficient for CNHC in brane world.
