  Following [1] we further apply the octonionic structure to supersymmetric
D=11 $M$-theory. We consider the octonionic $2^{n+1} \times 2^{n+1}$ Dirac
matrices describing the sequence of Clifford algebras with signatures ($9+n,n$)
($n=0,1,2, ...$) and derive the identities following from the octonionic
multiplication table. The case $n=1$ ($4\times 4$ octonion-valued matrices) is
used for the description of the D=11 octonionic $M$ superalgebra with 52 real
bosonic charges; the $n=2$ case ($8 \times 8$ octonion-valued matrices) for the
D=11 conformal $M$ algebra with 232 real bosonic charges. The octonionic
structure is described explicitly for $n=1$ by the relations between the 528
Abelian O(10,1) tensorial charges $Z_\mu Z_{\mu\nu}, Z_{\mu \gt... \mu_5}$ of
the $M$-superalgebra. For $n=2$ we obtain 2080 real non-Abelian bosonic
tensorial charges $Z_{\mu\nu}, Z_{\mu_1 \mu_2 \mu_3}, Z_{\mu_1 ... \mu_6}$
which, suitably constrained describe the generalized D=11 octonionic conformal
algebra. Further, we consider the supersymmetric extension of this octonionic
conformal algebra which can be described as D=11 octonionic superconformal
algebra with a total number of 64 real fermionic and 239 real bosonic
generators.
