  Orbifold branes are studied in the framework of the 11-dimensional
Horava-Witten heterotic M-Theory. It is found that the effective cosmological
constant can be easily lowered to its current observational value by the
mechanism of large extra dimensions. The domination of this constant over the
evolution of the universe is only temporarily. Due to the interaction of the
bulk and the branes, the universe will be in its decelerating expansion phase
again in the future, whereby all problems connected with a far future de Sitter
universe are resolved.
