We analyze the structure of heterotic M-theory on K3 orbifolds by presenting
a comprehensive sequence of M-theoretic models constructed on the basis of
local anomaly cancellation. This is facilitated by extending the technology
developed in our previous papers to allow one to determine "twisted" sector
states in non-prime orbifolds. These methods should naturally generalize to
four-dimensional models, which are of potential phenomenological interest.Comment: 58 pages, LaTe