  We study conformal Killing forms on compact 6-dimensional nearly K\"ahler
manifolds. Our main result concerns forms of degree 3. Here we give a
classification showing that all conformal Killing 3-forms are linear
combinations of $d \omega$ and its Hodge dual $* d\omega$ where $\omega$ is the
fundamental 2-form of the nearly K\"ahler structure. The proof is based on a
fundamental integrability condition for conformal Killing forms. We have
partial results in the case of conformal Killing 2-forms. In particular we show
the non-existence of J-anti-invariant Killing 2-forms.
