  We investigate the most general N=1 graded extension of the Poincare algebra,
and find the corresponding supersymmetry transformations and the associated
superspaces. We find that the supersymmetry for which {Q,Q} = P is not special,
and in fact must be treated democratically with a whole class of
supersymmetries. We show that there are two distinct types of grading, and a
new class of general spinors is defined. The associated superspaces are shown
to be either of the usual type, or flat with no torsion. p-branes are discussed
in these general superspaces and twelve dimensions emerges as maximal. New
types of brane are discovered which could explain many features of the standard
p-brane theories.
