  We consider Minkowski compactifications of M-theory on generic
seven-dimensional manifolds. After analyzing the conditions on the four-form
flux, we establish a set of relations between the components of the intrinsic
torsion of the internal manifold and the components of the four-form flux
needed for preserving supersymmetry. The existence of two nowhere vanishing
vectors on any seven-manifold with G_2 structure plays a crucial role in our
analysis, leading to the possibility of four-dimensional compactifications with
N=1 and N=2 supersymmetry.
