  For a real or complex semisimple Lie group $G$ and two nested parabolic
subgroups $Q\subset P\subset G$, we study parabolic geometries of type $(G,Q)$.
Associated to the group $P$, we introduce a class of relative natural bundles
and relative tractor bundles and construct some basic invariant differential
operators on such bundles. We define a (rather weak) notion of
"compressability" for operators acting on relative differential forms with
values in a relative tractor bundle. The we develop a general machinery which
converts a compressable operator to an operator on bundles associated to
completely reducible representations on relative Lie algebra homology groups.
  Applying this machinery to a specific compressable invariant differential
operator of order one, we obtain a relative version of BGG
(Bernstein--Gelfand--Gelfand) sequences. All our constructions apply in the
case $P=G$, producing new and simpler proofs in the case of standard BGG
sequences. We characterize cases in which the relative BGG sequences are
complexes or even fine resolutions of certain sheaves and describe these
sheaves. We show that this gives constructions of new invariant differential
operators as well as of new subcomplexes in certain curved BGG sequences. The
results are made explicit in the case of generalized path geometries.
