  It is shown that the integrability conditions that arise in the Null Surface
Formulation (NSF) of general relativity (GR) impose a field equation on the
local null surfaces which is equivalent to the vanishing of the Bach tensor.
This field equation is written explicitly to second order in a perturbation
expansion.
  The field equation is further simplified if asymptotic flatness is imposed on
the underlying space-time. The resulting equation determines the global null
surfaces of asymptotically flat, radiative space-times. It is also shown that
the source term of this equation is constructed from the free Bondi data at
future null infinity.
  Possible generalizations of this field equation are analyzed. In particular
we include other field equations for surfaces that have already appeared in the
literature which coincide with ours at a linear level. We find that the other
equations do not yield null surfaces for GR.
