In this work we present octonionic duality for membranes. We start with a d
iscussion on the relation of the Yang-Mills theories and the the supermembr
ane Hamiltonian in the light-cone gauge. We further derive the self-duality
equations for the membranes and discuss the integrability of the system in
7 and 3 dimensions. Finally, we present classical Euclidean time solutions
of these equations and examine the supersymmetries left intact by the self
-duality equations.