BPS states in M-theory and twistorial constituents

We provide a complete algebraic description of BPS states in M-theory in terms of primary constituents that we call BPS preons. We argue that any BPS state preserving $k$ of the 32 supersymmetries is a composite of (32-k) BPS preons. In particular, the BPS states corresponding to the basic M2 and M5 branes are composed of 16 BPS preons. By extending the M-algebra to a generalized D=11 conformal superalgebra $osp(1\mathrm{\mid }64)$ we relate the BPS preons with its fundamental representation, the D=11 supertwistors.