  We investigate the dynamics of a Bianchi I brane Universe in the presence of
a nonlocal anisotropic stress ${\cal P}_{\mu\nu}$ proportional to a "dark
energy" ${\cal U}$. Using this ansatz for the case ${\cal U} > 0$ we prove that
if a matter on a brane satisfies the equation of state $p=(\gamma-1)\rho$ with
$\gamma \le 4/3$ then all such models isotropize. For $\gamma > 4/3$
anisotropic future asymptotic states are found. We also describe the past
asymptotic regimes for this model.
