  We examine free orientation-reversing group actions on orientable
handlebodies, and free actions on nonorientable handlebodies. A classification
theorem is obtained, giving the equivalence classes and weak equivalence
classes of free actions in terms of algebraic invariants that involve Nielsen
equivalence. This is applied to describe the sets of free actions in various
cases, including a complete classification for many (and conjecturally all)
cases above the minimum genus. For abelian groups, the free actions are
classified for all genera.
