  Quaternionic and octonionic spinors are introduced and their fundamental
properties (such as the space-times supporting them) are reviewed. The
conditions for the existence of their associated Dirac equations are analyzed.
Quaternionic and octonionic supersymmetric algebras defined in terms of such
spinors are constructed. Specializing to the D=11-dimensional case, the
relation of both the quaternionic and the octonionic supersymmetries with the
ordinary M-algebra are discussed.
