  We consider compactifications of M-theory on 7-manifolds in the presence of
4-form fluxes, which leave at least four supercharges unbroken. Supersymmetric
vacua admit G-structures and we discuss the cases of G_2-, SU(3)- as well as
SU(2)-structures. We derive the constraints on the fluxes imposed by
supersymmetry and determine the flux components that fix the resulting
4-dimensional cosmological constant (i.e. superpotential).
