  BGG-sequences offer a uniform construction for invariant differential
operators for a large class of geometric structures called parabolic
geometries. For locally flat geometries, the resulting sequences are complexes,
but in general the compositions of the operators in such a sequence are
nonzero. In this paper, we show that under appropriate torsion freeness and/or
semi-flatness assumptions certain parts of all BGG sequences are complexes.
  Several examples of structures, including quaternionic structures,
hypersurface type CR structures and quaternionic contact structures are
discussed in detail. In the case of quaternionic structures we show that
several families of complexes obtained in this way are elliptic.
