We develop the BPS preon conjecture to analyze the supersymmetric solutions of D = 11 supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method (G = GL(32, R), SL(32, R) or Sp(32, R)) to analyze their associated generalized holonomies. As a first application we derive here the equations determining the generalized holonomies of ν = k/32 supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic (ν = 31/32) solutions of the standard D = 11 supergravity. We also show that there exist elementary preonic solutions, i.e. solutions preserving 31 out of 32 supersymmetries in a Chern-Simons type supergravity. We present as well a family of worldvolume actions describing the motion of pointlike and extended BPS preons in the background of a D'Auria-Fré type OSp(1|32)-related supergravity model. We discuss the possible implications for M-theory.