  The classification of the octonionic realizations of the one-dimensional
extended supersymmetries is here furnished. These are non-associative
realizations which, albeit inequivalent, are put in correspondence with a
subclass of the already classified associative representations for 1D extended
supersymmetries. Examples of dynamical systems invariant under octonionic
realizations of the extended supersymmetries are given. We cite among the
others the octonionic spinning particles, the N=8 KdV, etc. Possible
applications to supersymmetric systems arising from dimensional reduction of
the octonionic superstring and M-theory are mentioned.
