  A 2-form on a quaternionic-Kahler manifold (M, g) is called compatible (with
the quaternionic structure) if it is a section of the direct sum bundle S^2(H)
\oplus S^2(E). We construct a connection D on S^2(H) \oplus S^2(E)\oplus TM,
which is a prolongation of the conformal-Killing operator acting on compatible
2-forms. We show that D is flat if and only if the quaternionic-Weyl tensor of
(M,g) is zero. Consequences of this result are developed. We construct a
skew-symmetric multiplication on the space of conformal-Killing 2-forms on
(M,g) and we study its properties in connection with the subspace of compatible
conformal-Killing 2-forms.
