  We find M-theory solutions with homogeneous fluxes for which the spacetime is
a lorentzian symmetric space. We show that generic solutions preserve sixteen
supersymmetries and that there are two special points in their moduli space of
parameters which preserve all thirty-two supersymmetries. We calculate the
symmetry superalgebra of all these solutions. We then construct various
M-theory and string theory branes with homogeneous fluxes and we also find new
homogeneous flux-brane solutions.
