  I present a construction of real or complex selfdual conformal 4-manifolds
(of signature (2,2) in the real case) from a natural gauge field equation on a
real or complex projective surface, the gauge group being the group of
diffeomorphisms of a real or complex 2-manifold. The 4-manifolds obtained are
characterized by the existence of a foliation by selfdual null surfaces of a
special kind. The classification by Dunajski and West of selfdual conformal
4-manifolds with a null conformal vector field is the special case in which the
gauge group reduces to the group of diffeomorphisms commuting with a vector
field, and I analyse the presence of compatible scalar-flat K\"ahler,
hypercomplex and hyperk\"ahler structures from a gauge-theoretic point of view.
In an appendix, I discuss the twistor theory of projective surfaces, which is
used in the body of the paper, but is also of independent interest.
