The equations of motion of the super five-brane in D = 11 dimensions a
re derived using the formalism of superembeddings. The equations descr
ibe highly nonlinear self-interactions of a tensor multiplet in the si
x dimensional worlsurface, and they have manifest worldsurface local s
upersymmetry. The geometry of the target space corresponds to D = 11 s
upergravity.