  Twistor space constructions and actions are given for full Yang-Mills and
conformal gravity using almost complex structures that are not, in general,
integrable. These are used as the basis of a derivation of the twistor-string
generating functionals for tree level perturbative scattering amplitudes of
Yang-Mills and conformal gravity. The derivation follows by expanding and
resumming the classical approximation to the path integral obtained from the
twistor action. It provides a basis for exploring whether the equivalence can
be made to extend beyond tree level and allows one to disentangle conformal
supergravity modes from the Yang-Mills modes.
