It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains $psl(4|4,mathbb R)$ superalgebr
a. In quantum theory this infinite-dimensional symmetry breaks down to $SL(4|4,mathbb R)$ one.
Equations of motion for the D0-brane on AdS_4 x CP^3 superbackground are shown to be classically integrable by extending the argument previously elaborated for the massless superparticle model.
Lax representation is elaborated for the equations of motion of massless superparticle on the AdS_4 x CP^3 superbackground that proves their classical integrability.
Motivated by the isomorphism between osp(4|6) superalgebra and D=3 N=6 superconformal algebra we consider the superstring action on the AdS_4 x CP^3 background parametrized by D=3 N=6 super-Poincare and CP^3 coordinates supplemented by the coordinate
s corresponoding to dilatation and superconformal generators. It is also discussed the relation between the degeneracy of fermionic equations of motion and the action kappa-invariance in the framework of the supercoset approach.
Canonical description of the D=10 superstring action involving supertwistor variables generalizing Penrose-Ferber supertwistors is developed. Primary and secondary constraints are identified and arranged into the first- and second-class sets. Dirac b
rackets are introduced and the deformation of the Poisson bracket algebra of the first-class constraints is studied. The role of the deformation parameter is played by alpha.
