  We derive the most general flux-induced superpotential for N=1 M-theory
compactifications on seven-dimensional manifolds with SU(3) structure. Imposing
the appropriate boundary conditions, this result applies for heterotic
M-theory. It is crucial for the latter to consider SU(3) and not G_2 group
structure on the seven-dimensional internal space. For a particular background
that differs from CY(3) x S^1/Z_2 only by warp factors, we investigate the
flux-generated scalar potential as a function of the orbifold length. We find a
positive cosmological constant minimum, however at an undesirably large value
of this length. Hence the flux superpotential alone is not enough to stabilize
the orbifold length at a de Sitter vacuum. But it does modify substantially the
interplay between the previously studied non-perturbative effects, possibly
reducing the significance of open membrane instantons while underlining the
importance of gaugino condensation.
