  In this paper the notion of an M-th order invariant bilinear differential
pairing is introduced and a formal definition is given. If the manifold has an
AHS structure, then various first order pairings are constructed. This yields a
classification of all first order invariant bilinear differential pairings on
homogeneous spaces with an AHS structure except for certain totally degenerate
cases. Moreover higher order invariant bilinear differential pairings are
constructed on these homogeneous spaces which leads to a classification on
complex projective space for the non degenerate cases. A degenerate case
corresponds to the existence of an invariant linear differential operator.
