  We study open supermembranes in 11 dimensional rigid superspace with 6
dimensional topological defects (M-theory five-branes). After rederiving in the
Green-Schwarz formalism the boundary conditions for open superstrings in the
type IIA theory, we determine the boundary conditions for open supermembranes
by imposing kappa symmetry and invariance under a fraction of 11 dimensional
supersymmetry. The result seems to imply the self-duality of the three-form
field strength on the five-brane world volume. We show that the light-cone
gauge formulation is regularized by a dimensional reduction of a 6 dimensional
N=1 super Yang-Mills theory with the gauge group SO(N\to\infty). We also
analyze the SUSY algebra and BPS states in the light-cone gauge.
