  A formalism for calculating the open supermembrane contribution to the
non-perturbative superpotential of moduli in heterotic M-theory is presented.
This is explicitly applied to the Calabi-Yau (1,1)-moduli and the separation
modulus of the end-of-the-world BPS three-branes, whose non-perturbative
superpotential is computed. The role of gauge bundles on the boundaries of the
open supermembranes is discussed in detail, and a topological criterion
presented for the associated superpotential to be non-vanishing.
