  We introduce a new class of gauge field theories in any complex dimension,
based on algebra-valued (p,q)-forms on complex n-manifolds. These theories are
holomorphic analogs of the well-known Chern-Simons and BF topological theories
defined on real manifolds. We introduce actions for different special
holomorphic BF theories on complex, Kahler and Calabi-Yau manifolds and
describe their gauge symmetries. Candidate observables, topological invariants
and relations to integrable models are briefly discussed.
