  In the context of string theory, axions appear to provide the most plausible
solution of the strong CP problem. However, as has been known for a long time,
in many string-based models, the axion coupling parameter F_a is several orders
of magnitude higher than the standard cosmological bounds. We re-examine this
problem in a variety of models, showing that F_a is close to the GUT scale or
above in many models that have GUT-like phenomenology, as well as some that do
not. On the other hand, in some models with Standard Model gauge fields
supported on vanishing cycles, it is possible for F_a to be well below the GUT
scale.
