Twistor variational principle for null strings

I present a twistor action functional for null 2-surfaces (null strings) in 4D Minkowski spacetime. The proposed formulation is reparametrization invariant and free of algebraic and differential constraints. Proposed approach results in derivation of evolution equations for the null strings. It is shown that non-geodesic null strings are contained in the presented formalism. A discussion of the problem of minimality for 2-surfaces with degenerate induced metric is given. I also speculate on the possible description of strings (time-like 2-surfaces) and conventional (space-like) 2-surfaces.