  New universal invariant operators are introduced in a class of geometries
which include the quaternionic structures and their generalisations as well as
4-dimensional conformal (spin) geometries. It is shown that, in a broad sense,
all invariants and invariant operators arise from these universal operators and
that they may be used to reduce all invariants problems to corresponding
algebraic problems involving homomorphisms between modules of certain parabolic
subgroups of Lie groups. Explicit application of the operators is illustrated
by the construction of all non-standard operators between exterior forms on a
large class of the geometries which includes the quaternionic structures.
