  We study the behavior of spatially homogeneous brane-worlds close to the
initial singularity in the presence of both local and nonlocal stresses. It is
found that the singularity in these brane-worlds can be locally either
isotropic or anisotropic. We then investigate the Weyl curvature conjecture,
according to which some measure of the Weyl curvature is related to a
gravitational entropy. In particular, we study the Weyl curvature conjecture on
the brane with respect to the dimensionless ratio of the Weyl invariant and the
Ricci square and the measure proposed by Gr{\o}n and Hervik. We also argue that
the Weyl curvature conjecture should be formulated on brane
  (i.e., in the four-dimensional context).
