BPS states in M theory and twistorial constituents.

We provide a complete algebraic description of Bogomol'nyi-Prasad-Sommerfield (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.