  This is the second in a series of articles surveying the body of work on the
model theory of S-acts over a monoid S. The first concentrated on the theory of
regular S-acts. Here we review the material on model-theoretic properties of
free, projective, and (strongly, weakly) flat S-acts. We consider questions of
axiomatizability, completeness, model completeness, and stability for these
classes. Most but not all of the results have already appeared; we remark that
the description of those monoids S such that the class of free left S-acts is
axiomatizable, is new.
