  We first construct the Rozansky-Witten model coupled to BF theory and
Chern-Simons theory using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ)
method. Then we apply the machinery developed in some earlier papers about AKSZ
theories and characteristic classes to these concrete models: the
BF-Rozansky-Witten model and the Chern-Simons-Rozansky-Witten model. In the
former case, we obtain characteristic classes on the target hyperKahler
manifold equipped with a group action as a generalization of the original
Rozansky-Witten classes. We also give the prescription for similar classes
associated with a holomorphic symplectic manifold and demonstrate the
invariance of such classes explicitly.
