Generalized Superconformal Symmetries and Supertwistor Dynamics

We show that in the supersymmetry framework described by a Poincar'{e} superalgebra with tensorial central charges the role of generalized superconformal symmetry which contains all these central charges is played by $OSp(1\mathrm{\mid }{2}^k)$, where k=3 for D=4. Following [1,2] we describe the free supertwistor model for $OSp(1\mathrm{\mid }8)$. It appears that in such a scheme the tensorial central charges satisfy additional relations and the model describes the tower of supersymmetric massless states with an arbitrary (integer and half–integer) helicity spectrum.