  We describe generalized D=11 Poincar\'{e} and conformal supersymmetries. The
corresponding generalization of twistor and supertwistor framework is outlined
with $OSp(1|64)$ superspinors describing BPS preons. The $\frac{k}{32}$ BPS
states as composed out of $n=32 - k$ preons are introduced, and basic ideas
concerning BPS preon dynamics is presented. The lecture is based on results
obtained by J.A. de Azcarraga, I. Bandos, J.M. Izquierdo and the author$^1$.
