  We examine the possibility that the strong CP problem is solved by
string-theoretic axions in strong-coupling limit of the E_8 x E_8 heterotic
string theory (M-theory). We first discuss some generic features of gauge
kinetic functions in compactified M-theory, and examine in detail the axion
potential induced by the explicit breakings other than the QCD anomaly of the
non-linear U(1)_{PQ} symmetries of string-theoretic axions. It is argued based
on supersymmetry and discrete gauge symmetries that if the compactification
radius is large enough, there can be a U(1)_{PQ}-symmetry whose breaking other
than the QCD anomaly, whatever its microscopic origin is, is suppressed enough
for the axion mechanism to work. Phenomenological viability of such a large
radius crucially depends upon the quantized coefficients in gauge kinetic
functions. We note that the large radius required for the axion mechanism is
viable only in a limited class of models. For instance, for compactifications
on a smooth Calabi-Yau manifold with a vanishing second E_8 field strength, it
is viable only when the quantized flux of the antisymmetric tensor field in
M-theory has a minimal nonzero value. It is also stressed that this large
compactification radius allows the QCD axion in M-theory to be cosmologically
viable in the presence of a late time entropy production.
