  The effective four-dimensional supergravity of M-theory compactified on the
orbifold S^1/Z_2 and a Calabi-Yau threefold includes in general moduli
supermultiplets describing massless modes of five-branes. For each brane, one
of these fields corresponds to fluctuations along the interval. The five-brane
also leads to modifications of the anomaly-cancelling terms in the
eleven-dimensional theory, including gauge contributions located on their
world-volumes. We obtain the interactions of the brane "interval modulus"
predicted by these five-brane-induced anomaly-cancelling terms and we construct
their effective supergravity description. In the condensed phase, these
interaction terms generate an effective non-perturbative superpotential which
can also be interpreted as instanton effects of open membranes stretching
between five-branes and the S^1/Z_2 fixed hyperplanes. Aspects of the vacuum
structure of the effective supergravity are also briefly discussed.
