  We present a twistor description for null two-surfaces (null strings) in 4D
Minkowski space-time. The Lagrangian density for a variational principle is
taken as a surface-forming null bivector. The proposed formulation is
reparametrization invariant and free of any algebraic and differential
constraints. The spinor formalism of Cartan-Penrose allows us to derive a
non-linear evolution equation for the world-sheet coordinate. An example of
null two-surface given by the two-dimensional self-intersection (caustic) of a
null hypersurface is studied.
