  We investigate the Killing spinor equations of IIB supergravity for one
Killing spinor. We show that there are three types of orbits of Spin(9,1) in
the space of Weyl spinors which give rise to Killing spinors with stability
subgroups $Spin(7)\ltimes \bR^8$, $SU(4)\ltimes \bR^8$ and $G_2$. We solve the
Killing spinor equations for the $Spin(7)\ltimes \bR^8$ and $SU(4)\ltimes
\bR^8$ invariant spinors, give the fluxes in terms of the geometry and
determine the conditions on the spacetime geometry imposed by supersymmetry. In
both cases, the spacetime admits a null, self-parallel, Killing vector field.
We also apply our formalism to examine a class of $SU(4)\ltimes \bR^8$
backgrounds which admit one and two pure spinors as Killing spinors and
investigate the geometry of the spacetimes.
