  We study the hidden symmetries of the fermionic sector of D=11 supergravity,
and the role of K(E10) as a generalised `R-symmetry'. We find a consistent
model of a massless spinning particle on an E10/K(E10) coset manifold whose
dynamics can be mapped onto the fermionic and bosonic dynamics of D=11
supergravity in the near space-like singularity limit. This E10-invariant
superparticle dynamics might provide the basis of a new definition of M-theory,
and might describe the `de-emergence' of space-time near a cosmological
singularity.
