  Recently we have considered supertwistor reformulation of the D=4 N=1,2
superstring action that comprises Newman-Penrose dyad components and is
classically equivalent to the Green-Schwarz one. It was shown that in the
covariant kappa-symmetry gauge the supertwistor representation of the string
action simplifies. Here we analyze its Hamiltonian formulation, classify the
constraints on the phase-space variables, and find the covariant set of
generators of the gauge symmetries. Quantum symmetries of the supertwistor
representation of the string action are examined applying the world-sheet CFT
technique. Considered are various generalizations of the model from the
perspective of their possible relation to known twistor superstring models.
