During recent years there has been an activity in the development of a, so called, twistor-like, doubly supersymmetric approach for describing superparticles and superstrings [1]–[8]. The aim of the approach is to provide with clear geometrical meaning an obscure local fermionic symmetry (k-symmetry) of superparticles and superstrings [9, 10], which plays an essential role in quantum consistency of the theory. At the same time this local fermionic symmetry causes problems with performing the covariant Hamiltonian analysis and quantization of the th eories. This is due to the fact that the first–class constraints corresponding to the k-symmetry form an infinit reducible set, and in a conventional formulation of superparticles and superstrings (see [10] and references therein) it turned out impossible to single out an irreducible set of the fermionic first–class constraints in a Lorentz covariant way. So the idea was to replace the k-symmetry by a local extended supersymmetry on the worldsheet by constructing superparticle and superstring models which would be manifestly supersymmetric in a target superspace and on the world-sheet with the number of local supersymmetries being equal to the number of independet k-symmetry transformations, that is n = D - 2 in a space–time with the dimension D = 3, 4, 6 and 10. Note that it is just in these space–time dimensions the classical theory of Green–Schwarz superstrings may be formulated [10], and twistor relations [11] take place.

The doubly supersymmetric formulation provides the ground for natural incorporating twistors into the structure of supersymmetric theories.