  We show how the theory of invariant principal bundle connections for
reductive homogeneous spaces can be applied to determine the holonomy of
generalised Killing spinor covariant derivatives of the form $D= \nabla +
\Omega$ in a purely algebraic and algorithmic way, where $\Omega : TM
\rightarrow \Lambda^*(TM)$ is a left-invariant homomorphism. Specialising this
to the case of symmetric M-theory backgrounds (i.e. $(M,g,F)$ with $(M,g)$ a
symmetric space and $F$ an invariant closed 4-form), we derive several criteria
for such a background to preserve some supersymmetry and consequently find all
supersymmetric symmetric M-theory backgrounds.
