  Twistor forms are a natural generalization of conformal vector fields on
Riemannian manifolds. They are defined as sections in the kernel of a
conformally invariant first order differential operator. We study twistor forms
on compact Kaehler manifolds and give a complete description up to special
forms in the middle dimension. In particular, we show that they are closely
related to Hamiltonian 2-forms. This provides the first examples of compact
Kaehler manifolds with non-parallel twistor forms in any even degree.
