  It is shown that the $M$-algebra related with the $M$ theory comes in two
variants. Besides the standard $M$ algebra based on the real structure, an
alternative octonionic formulation can be consistently introduced. This second
variant has striking features. It involves only 52 real bosonic generators
instead of 528 of the standard $M$ algebra and moreover presents a novel and
surprising feature, its octonionic $M5$ (super-5-brane) sector is no longer
independent, but coincides with the octonionic $M1$ and $M2$ sectors. This is
in consequence of the non-associativity of the octonions. An octonionic version
of the superconformal $M$-algebra also exists. It is given by $OSp(1,8|{\bf
O})$ and admits 239 bosonic and 64 fermionic generators. It is speculated that
the octonionic $M$-algebra can be related to the exceptional Lie and Jordan
algebras that apparently play a special role in the Theory Of Everything.
