  We discuss non-perturbative phase transitions, within the context of
heterotic M-theory, which occur when all, or part, of the wrapped five-branes
in the five-dimensional bulk space come into direct contact with a boundary
brane. These transitions involve the transformation of the five-brane into a
``small instanton'' on the Calabi-Yau space at the boundary brane, followed by
the ``smoothing out'' of the small instanton into a holomorphic vector bundle.
Small instanton phase transitions change the number of families, the gauge
group or both on the boundary brane, depending upon whether a base component,
fiber component or both components of the five-brane class are involved in the
transition. We compute the conditions under which a small instanton phase
transition can occur and present a number of explicit, phenomenologically
relevant examples.
